LMFDB - Embedded newform 624.2.ch.a.19.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(19,624)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("624.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.ch (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.47
Character	$\chi$	$=$	624.19
Dual form			624.2.ch.a.427.47

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25238 - 0.656929i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.13689 - 1.64544i) q^{4} +3.89484i q^{5} +(-0.958683 - 1.03968i) q^{6} +(-0.475163 + 1.77333i) q^{7} +(0.342870 - 2.80757i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(1.25238 - 0.656929i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.13689 - 1.64544i) q^{4} +3.89484i q^{5} +(-0.958683 - 1.03968i) q^{6} +(-0.475163 + 1.77333i) q^{7} +(0.342870 - 2.80757i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.55864 + 4.87781i) q^{10} +(1.67516 + 0.967155i) q^{11} +(-1.88363 - 0.672277i) q^{12} +(3.59307 + 0.299789i) q^{13} +(0.569871 + 2.53303i) q^{14} +(3.76213 - 1.00806i) q^{15} +(-1.41497 - 3.74137i) q^{16} +(0.562272 - 0.324628i) q^{17} +(-0.756124 + 1.19511i) q^{18} +(5.51859 - 3.18616i) q^{19} +(6.40875 + 4.42800i) q^{20} +1.83589 q^{21} +(2.73328 + 0.110779i) q^{22} +(6.22556 + 3.59433i) q^{23} +(-2.80064 + 0.395465i) q^{24} -10.1698 q^{25} +(4.69681 - 1.98494i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.37771 + 2.79793i) q^{28} +(-6.54948 + 1.75493i) q^{29} +(4.04938 - 3.73392i) q^{30} +(-0.609612 - 0.609612i) q^{31} +(-4.22989 - 3.75607i) q^{32} +(0.500636 - 1.86840i) q^{33} +(0.490918 - 0.775929i) q^{34} +(-6.90685 - 1.85069i) q^{35} +(-0.161852 + 1.99344i) q^{36} +(0.277700 - 0.480990i) q^{37} +(4.81826 - 7.61559i) q^{38} +(-0.640380 - 3.54823i) q^{39} +(10.9350 + 1.33543i) q^{40} +(-8.45842 + 2.26643i) q^{41} +(2.29922 - 1.20605i) q^{42} +(-6.12658 - 1.64161i) q^{43} +(3.49587 - 1.65684i) q^{44} +(-1.94742 - 3.37303i) q^{45} +(10.1580 + 0.411696i) q^{46} +(2.00724 - 2.00724i) q^{47} +(-3.24767 + 2.33510i) q^{48} +(3.14325 + 1.81476i) q^{49} +(-12.7364 + 6.68085i) q^{50} +(-0.459093 - 0.459093i) q^{51} +(4.57820 - 5.57136i) q^{52} +(-3.59120 + 3.59120i) q^{53} +(1.35008 + 0.421044i) q^{54} +(-3.76692 + 6.52449i) q^{55} +(4.81583 + 1.94208i) q^{56} +(-4.50591 - 4.50591i) q^{57} +(-7.04954 + 6.50037i) q^{58} +(2.05044 - 1.18382i) q^{59} +(2.61842 - 7.33643i) q^{60} +(2.27274 - 8.48197i) q^{61} +(-1.16393 - 0.362991i) q^{62} +(-0.475163 - 1.77333i) q^{63} +(-7.76488 - 1.92526i) q^{64} +(-1.16763 + 13.9944i) q^{65} +(-0.600422 - 2.66882i) q^{66} +(-11.4041 - 6.58414i) q^{67} +(0.105083 - 1.29425i) q^{68} +(1.86056 - 6.94371i) q^{69} +(-9.86574 + 2.21956i) q^{70} +(11.6842 + 3.13077i) q^{71} +(1.10685 + 2.60286i) q^{72} +(-0.704272 + 0.704272i) q^{73} +(0.0318079 - 0.784809i) q^{74} +(2.63214 + 9.82328i) q^{75} +(1.03137 - 12.7028i) q^{76} +(-2.51106 + 2.51106i) q^{77} +(-3.13293 - 4.02303i) q^{78} +0.269030i q^{79} +(14.5721 - 5.51109i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-9.10424 + 8.39500i) q^{82} -11.0177i q^{83} +(2.08720 - 3.02085i) q^{84} +(1.26437 + 2.18996i) q^{85} +(-8.75121 + 1.96882i) q^{86} +(3.39026 + 5.87210i) q^{87} +(3.28972 - 4.37152i) q^{88} +(-3.77886 - 14.1029i) q^{89} +(-4.65475 - 2.94499i) q^{90} +(-2.23892 + 6.22925i) q^{91} +(12.9920 - 6.15746i) q^{92} +(-0.431061 + 0.746619i) q^{93} +(1.19520 - 3.83243i) q^{94} +(12.4096 + 21.4940i) q^{95} +(-2.53330 + 5.05790i) q^{96} +(-10.2805 - 2.75464i) q^{97} +(5.12869 + 0.207863i) q^{98} -1.93431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q+O(q^{10}) $ 224 * q	$ 224 q - 8 q^{10} - 32 q^{14} - 48 q^{16} - 12 q^{20} + 8 q^{22} + 12 q^{24} - 224 q^{25} - 16 q^{26} - 52 q^{28} + 40 q^{32} + 64 q^{34} - 40 q^{38} - 40 q^{40} - 16 q^{43} + 24 q^{44} + 16 q^{46} - 16 q^{50} - 16 q^{52} - 32 q^{55} - 20 q^{56} - 32 q^{58} + 96 q^{59} - 64 q^{60} - 24 q^{68} - 48 q^{70} + 64 q^{71} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 76 q^{76} - 24 q^{78} + 100 q^{80} + 112 q^{81} + 48 q^{82} - 64 q^{86} - 60 q^{88} - 16 q^{89} + 40 q^{91} - 48 q^{92} + 64 q^{94} - 56 q^{98}+O(q^{100}) $ 224 * q - 8 * q^10 - 32 * q^14 - 48 * q^16 - 12 * q^20 + 8 * q^22 + 12 * q^24 - 224 * q^25 - 16 * q^26 - 52 * q^28 + 40 * q^32 + 64 * q^34 - 40 * q^38 - 40 * q^40 - 16 * q^43 + 24 * q^44 + 16 * q^46 - 16 * q^50 - 16 * q^52 - 32 * q^55 - 20 * q^56 - 32 * q^58 + 96 * q^59 - 64 * q^60 - 24 * q^68 - 48 * q^70 + 64 * q^71 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 76 * q^76 - 24 * q^78 + 100 * q^80 + 112 * q^81 + 48 * q^82 - 64 * q^86 - 60 * q^88 - 16 * q^89 + 40 * q^91 - 48 * q^92 + 64 * q^94 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.25238	−	0.656929i	0.885563	−	0.464519i
$2$	1.25238	−	0.656929i	0.885563	−	0.464519i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	1.13689	−	1.64544i	0.568444	−	0.822722i
$5$			3.89484i			1.74183i	0.491436	+	0.870914i	$0.336472\pi$
$5$			3.89484i			1.74183i	−0.491436	+	0.870914i	$0.663528\pi$
$6$	−0.958683	−	1.03968i	−0.391381	−	0.424446i
$7$	−0.475163	+	1.77333i	−0.179595	+	0.670257i	0.816128	+	0.577870i	$0.196116\pi$
$7$	−0.475163	+	1.77333i	−0.179595	+	0.670257i	−0.995723	+	0.0923863i	$0.970551\pi$
$8$	0.342870	−	2.80757i	0.121223	−	0.992625i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	2.55864	+	4.87781i	0.809112	+	1.54250i
$11$	1.67516	+	0.967155i	0.505080	+	0.291608i	0.730809	−	0.682582i	$-0.239143\pi$
$11$	1.67516	+	0.967155i	0.505080	+	0.291608i	−0.225729	+	0.974190i	$0.572476\pi$
$12$	−1.88363	−	0.672277i	−0.543756	−	0.194070i
$13$	3.59307	+	0.299789i	0.996537	+	0.0831464i
$13$	3.59307	+	0.299789i	0.996537	+	0.0831464i
$14$	0.569871	+	2.53303i	0.152305	+	0.676980i
$15$	3.76213	−	1.00806i	0.971378	−	0.260280i
$16$	−1.41497	−	3.74137i	−0.353743	−	0.935343i
$17$	0.562272	−	0.324628i	0.136371	−	0.0787338i	−0.430262	−	0.902704i	$-0.641579\pi$
$17$	0.562272	−	0.324628i	0.136371	−	0.0787338i	0.566633	+	0.823970i	$0.308246\pi$
$18$	−0.756124	+	1.19511i	−0.178220	+	0.281689i
$19$	5.51859	−	3.18616i	1.26605	−	0.730955i	0.291812	−	0.956476i	$-0.405742\pi$
$19$	5.51859	−	3.18616i	1.26605	−	0.730955i	0.974238	+	0.225521i	$0.0724084\pi$
$20$	6.40875	+	4.42800i	1.43304	+	0.990131i
$21$	1.83589			0.400624
$22$	2.73328	+	0.110779i	0.582738	+	0.0236181i
$23$	6.22556	+	3.59433i	1.29812	+	0.749469i	0.980079	−	0.198609i	$-0.0636423\pi$
$23$	6.22556	+	3.59433i	1.29812	+	0.749469i	0.318039	+	0.948078i	$0.396976\pi$
$24$	−2.80064	+	0.395465i	−0.571679	+	0.0807239i
$25$	−10.1698			−2.03396
$26$	4.69681	−	1.98494i	0.921120	−	0.389279i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.37771	+	2.79793i	0.449345	+	0.528760i
$29$	−6.54948	+	1.75493i	−1.21621	+	0.325882i	−0.809195	−	0.587541i	$-0.800096\pi$
$29$	−6.54948	+	1.75493i	−1.21621	+	0.325882i	−0.407013	+	0.913423i	$0.633429\pi$
$30$	4.04938	−	3.73392i	0.739311	−	0.681718i
$31$	−0.609612	−	0.609612i	−0.109489	−	0.109489i	0.650240	−	0.759729i	$-0.274668\pi$
$31$	−0.609612	−	0.609612i	−0.109489	−	0.109489i	−0.759729	+	0.650240i	$0.774668\pi$
$32$	−4.22989	−	3.75607i	−0.747746	−	0.663985i
$33$	0.500636	−	1.86840i	0.0871496	−	0.325247i
$34$	0.490918	−	0.775929i	0.0841917	−	0.133071i
$35$	−6.90685	−	1.85069i	−1.16747	−	0.312823i
$36$	−0.161852	+	1.99344i	−0.0269753	+	0.332240i
$37$	0.277700	−	0.480990i	0.0456536	−	0.0790743i	−0.842296	−	0.539016i	$-0.818796\pi$
$37$	0.277700	−	0.480990i	0.0456536	−	0.0790743i	0.887949	+	0.459942i	$0.152130\pi$
$38$	4.81826	−	7.61559i	0.781625	−	1.23541i
$39$	−0.640380	−	3.54823i	−0.102543	−	0.568171i
$40$	10.9350	+	1.33543i	1.72898	+	0.211150i
$41$	−8.45842	+	2.26643i	−1.32098	+	0.353956i	−0.849346	−	0.527836i	$-0.823003\pi$
$41$	−8.45842	+	2.26643i	−1.32098	+	0.353956i	−0.471637	+	0.881793i	$0.656337\pi$
$42$	2.29922	−	1.20605i	0.354778	−	0.186097i
$43$	−6.12658	−	1.64161i	−0.934295	−	0.250344i	−0.240610	−	0.970622i	$-0.577347\pi$
$43$	−6.12658	−	1.64161i	−0.934295	−	0.250344i	−0.693685	+	0.720278i	$0.744014\pi$
$44$	3.49587	−	1.65684i	0.527022	−	0.249778i
$45$	−1.94742	−	3.37303i	−0.290305	−	0.502822i
$46$	10.1580	+	0.411696i	1.49771	+	0.0607013i
$47$	2.00724	−	2.00724i	0.292786	−	0.292786i	−0.545394	−	0.838180i	$-0.683620\pi$
$47$	2.00724	−	2.00724i	0.292786	−	0.292786i	0.838180	+	0.545394i	$0.183620\pi$
$48$	−3.24767	+	2.33510i	−0.468760	+	0.337042i
$49$	3.14325	+	1.81476i	0.449036	+	0.259251i
$50$	−12.7364	+	6.68085i	−1.80120	+	0.944814i
$51$	−0.459093	−	0.459093i	−0.0642859	−	0.0642859i
$52$	4.57820	−	5.57136i	0.634882	−	0.772609i
$53$	−3.59120	+	3.59120i	−0.493290	+	0.493290i	−0.909341	−	0.416051i	$-0.863414\pi$
$53$	−3.59120	+	3.59120i	−0.493290	+	0.493290i	0.416051	+	0.909341i	$0.363414\pi$
$54$	1.35008	+	0.421044i	0.183723	+	0.0572968i
$55$	−3.76692	+	6.52449i	−0.507931	+	0.879762i
$56$	4.81583	+	1.94208i	0.643543	+	0.259521i
$57$	−4.50591	−	4.50591i	−0.596822	−	0.596822i
$58$	−7.04954	+	6.50037i	−0.925650	+	0.853540i
$59$	2.05044	−	1.18382i	0.266945	−	0.154121i	−0.360553	−	0.932739i	$-0.617412\pi$
$59$	2.05044	−	1.18382i	0.266945	−	0.154121i	0.627499	+	0.778618i	$0.284079\pi$
$60$	2.61842	−	7.33643i	0.338036	−	0.947128i
$61$	2.27274	−	8.48197i	0.290994	−	1.08600i	−0.653353	−	0.757053i	$-0.726638\pi$
$61$	2.27274	−	8.48197i	0.290994	−	1.08600i	0.944347	−	0.328951i	$-0.106695\pi$
$62$	−1.16393	−	0.362991i	−0.147820	−	0.0460999i
$63$	−0.475163	−	1.77333i	−0.0598649	−	0.223419i
$64$	−7.76488	−	1.92526i	−0.970610	−	0.240658i
$65$	−1.16763	+	13.9944i	−0.144827	+	1.73580i
$66$	−0.600422	−	2.66882i	−0.0739068	−	0.328509i
$67$	−11.4041	−	6.58414i	−1.39323	−	0.804381i	−0.399557	−	0.916708i	$-0.630836\pi$
$67$	−11.4041	−	6.58414i	−1.39323	−	0.804381i	−0.993671	+	0.112328i	$0.964169\pi$
$68$	0.105083	−	1.29425i	0.0127432	−	0.156951i
$69$	1.86056	−	6.94371i	0.223985	−	0.835924i
$70$	−9.86574	+	2.21956i	−1.17918	+	0.265288i
$71$	11.6842	+	3.13077i	1.38666	+	0.371555i	0.873536	−	0.486760i	$-0.161821\pi$
$71$	11.6842	+	3.13077i	1.38666	+	0.371555i	0.513125	+	0.858314i	$0.328488\pi$
$72$	1.10685	+	2.60286i	0.130443	+	0.306750i
$73$	−0.704272	+	0.704272i	−0.0824288	+	0.0824288i	−0.747119	−	0.664690i	$-0.768564\pi$
$73$	−0.704272	+	0.704272i	−0.0824288	+	0.0824288i	0.664690	+	0.747119i	$0.268564\pi$
$74$	0.0318079	−	0.784809i	0.00369759	−	0.0912322i
$75$	2.63214	+	9.82328i	0.303933	+	1.13429i
$76$	1.03137	−	12.7028i	0.118306	−	1.45711i
$77$	−2.51106	+	2.51106i	−0.286162	+	0.286162i
$78$	−3.13293	−	4.02303i	−0.354735	−	0.455518i
$79$			0.269030i			0.0302682i	0.999885	+	0.0151341i	$0.00481752\pi$
$79$			0.269030i			0.0302682i	−0.999885	+	0.0151341i	$0.995182\pi$
$80$	14.5721	−	5.51109i	1.62921	−	0.616159i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−9.10424	+	8.39500i	−1.00539	+	0.927073i
$83$		−	11.0177i		−	1.20935i	−0.796473	−	0.604674i	$-0.793303\pi$
$83$		−	11.0177i		−	1.20935i	0.796473	−	0.604674i	$-0.206697\pi$
$84$	2.08720	−	3.02085i	0.227732	−	0.329602i
$85$	1.26437	+	2.18996i	0.137141	+	0.237535i
$86$	−8.75121	+	1.96882i	−0.943667	+	0.212303i
$87$	3.39026	+	5.87210i	0.363474	+	0.629555i
$88$	3.28972	−	4.37152i	0.350685	−	0.466006i
$89$	−3.77886	−	14.1029i	−0.400558	−	1.49490i	−0.812103	−	0.583515i	$-0.801677\pi$
$89$	−3.77886	−	14.1029i	−0.400558	−	1.49490i	0.411544	−	0.911390i	$-0.364990\pi$
$90$	−4.65475	−	2.94499i	−0.490654	−	0.310429i
$91$	−2.23892	+	6.22925i	−0.234702	+	0.653003i
$92$	12.9920	−	6.15746i	1.35451	−	0.641959i
$93$	−0.431061	+	0.746619i	−0.0446989	+	0.0774208i
$94$	1.19520	−	3.83243i	0.123276	−	0.395285i
$95$	12.4096	+	21.4940i	1.27320	+	2.20524i
$96$	−2.53330	+	5.05790i	−0.258554	+	0.516220i
$97$	−10.2805	−	2.75464i	−1.04382	−	0.279691i	−0.304126	−	0.952632i	$-0.598364\pi$
$97$	−10.2805	−	2.75464i	−1.04382	−	0.279691i	−0.739697	+	0.672940i	$0.765031\pi$
$98$	5.12869	+	0.207863i	0.518076	+	0.0209974i
$99$	−1.93431			−0.194405
$100$	−11.5619	+	16.7339i	−1.15619	+	1.67339i
$101$	−6.56778	+	1.75983i	−0.653519	+	0.175110i	−0.570319	−	0.821423i	$-0.693180\pi$
$101$	−6.56778	+	1.75983i	−0.653519	+	0.175110i	−0.0831994	+	0.996533i	$0.526514\pi$
$102$	−0.876549	−	0.273365i	−0.0867912	−	0.0270672i
$103$		−	4.54344i		−	0.447678i	−0.974626	−	0.223839i	$-0.928141\pi$
$103$		−	4.54344i		−	0.447678i	0.974626	−	0.223839i	$-0.0718590\pi$
$104$	2.07363	−	9.98499i	0.203336	−	0.979109i
$105$			7.15050i			0.697817i
$106$	−2.13837	+	6.85670i	−0.207697	+	0.665982i
$107$	11.7831	−	3.15728i	1.13912	−	0.305226i	0.360521	−	0.932751i	$-0.382599\pi$
$107$	11.7831	−	3.15728i	1.13912	−	0.305226i	0.778596	+	0.627525i	$0.215932\pi$
$108$	1.96741	−	0.359603i	0.189314	−	0.0346028i
$109$	−9.56670			−0.916324			−0.458162	−	0.888869i	$-0.651492\pi$
$109$	−9.56670			−0.916324			−0.458162	+	0.888869i	$0.651492\pi$
$110$	−0.431465	+	10.6457i	−0.0411386	+	1.01503i
$111$	−0.536475	−	0.143748i	−0.0509199	−	0.0136440i
$112$	7.30704	−	0.731453i	0.690450	−	0.0691158i
$113$	8.54012	+	14.7919i	0.803387	+	1.39151i	0.917375	+	0.398025i	$0.130304\pi$
$113$	8.54012	+	14.7919i	0.803387	+	1.39151i	−0.113988	+	0.993482i	$0.536362\pi$
$114$	−8.60315	−	2.68303i	−0.805759	−	0.251288i
$115$	−13.9993	+	24.2476i	−1.30545	+	2.26110i
$116$	−4.55839	+	12.7719i	−0.423236	+	1.18585i
$117$	−3.26158	+	1.53691i	−0.301533	+	0.142087i
$118$	1.79024	−	2.82959i	0.164805	−	0.260485i
$119$	0.308502	+	1.15135i	0.0282804	+	0.105544i
$120$	−1.54027	−	10.9081i	−0.140607	−	0.995766i
$121$	−3.62922	−	6.28600i	−0.329929	−	0.571454i
$122$	−2.72573	−	12.1156i	−0.246776	−	1.09690i
$123$	4.37840	+	7.58361i	0.394787	+	0.683791i
$124$	−1.69614	+	0.310022i	−0.152318	+	0.0278408i
$125$		−	20.1356i		−	1.80098i
$126$	−1.76004	−	1.90873i	−0.156797	−	0.170043i
$127$	0.0725240	−	0.125615i	0.00643546	−	0.0111465i	−0.862790	−	0.505563i	$-0.831285\pi$
$127$	0.0725240	−	0.125615i	0.00643546	−	0.0111465i	0.869225	+	0.494416i	$0.164618\pi$
$128$	−10.9893	+	2.68982i	−0.971327	+	0.237749i
$129$			6.34271i			0.558444i
$130$	7.73104	+	18.2933i	0.678057	+	1.60443i
$131$	−14.3658	+	14.3658i	−1.25515	+	1.25515i	−0.301765	+	0.953382i	$0.597576\pi$
$131$	−14.3658	+	14.3658i	−1.25515	+	1.25515i	−0.953382	+	0.301765i	$0.902424\pi$
$132$	−2.50518	−	2.94793i	−0.218048	−	0.256584i
$133$	3.02789	+	11.3002i	0.262551	+	0.979855i
$134$	−18.6075	−	0.754151i	−1.60744	−	0.0651487i
$135$	−2.75407	+	2.75407i	−0.237033	+	0.237033i
$136$	−0.718628	−	1.68992i	−0.0616219	−	0.144910i
$137$	21.4066	+	5.73589i	1.82889	+	0.490050i	0.997813	−	0.0661045i	$-0.0210571\pi$
$137$	21.4066	+	5.73589i	1.82889	+	0.490050i	0.831079	+	0.556155i	$0.187724\pi$
$138$	−2.23140	−	9.91838i	−0.189950	−	0.844309i
$139$	−0.450262	+	1.68040i	−0.0381907	+	0.142530i	−0.982389	−	0.186849i	$-0.940173\pi$
$139$	−0.450262	+	1.68040i	−0.0381907	+	0.142530i	0.944198	+	0.329379i	$0.106839\pi$
$140$	−10.8975	+	9.26082i	−0.921009	+	0.782682i
$141$	−2.45836	−	1.41933i	−0.207031	−	0.119529i
$142$	16.6897	−	3.75479i	1.40057	−	0.315095i
$143$	5.72902	+	3.97725i	0.479085	+	0.332594i
$144$	3.09609	+	2.53264i	0.258007	+	0.211053i
$145$	−6.83517	−	25.5092i	−0.567630	−	2.11842i
$146$	−0.419356	+	1.34467i	−0.0347061	+	0.111286i
$147$	0.939387	−	3.50584i	0.0774793	−	0.289157i
$148$	−0.475729	−	1.00377i	−0.0391047	−	0.0825095i
$149$	15.3148	−	8.84201i	1.25464	−	0.724366i	0.282611	−	0.959234i	$-0.408799\pi$
$149$	15.3148	−	8.84201i	1.25464	−	0.724366i	0.972027	+	0.234869i	$0.0754660\pi$
$150$	9.74963	+	10.5733i	0.796054	+	0.863307i
$151$	−2.16315	−	2.16315i	−0.176034	−	0.176034i	0.613590	−	0.789625i	$-0.289725\pi$
$151$	−2.16315	−	2.16315i	−0.176034	−	0.176034i	−0.789625	+	0.613590i	$0.789725\pi$
$152$	−7.05319	−	16.5862i	−0.572090	−	1.34532i
$153$	−0.324628	+	0.562272i	−0.0262446	+	0.0454570i
$154$	−1.49520	+	4.79438i	−0.120487	+	0.386342i
$155$	2.37434	−	2.37434i	0.190712	−	0.190712i
$156$	−6.56645	−	2.98023i	−0.525737	−	0.238609i
$157$	−1.48211	−	1.48211i	−0.118285	−	0.118285i	0.645487	−	0.763772i	$-0.276655\pi$
$157$	−1.48211	−	1.48211i	−0.118285	−	0.118285i	−0.763772	+	0.645487i	$0.776655\pi$
$158$	0.176734	+	0.336927i	0.0140602	+	0.0268044i
$159$	4.39831	+	2.53937i	0.348809	+	0.201385i
$160$	14.6293	−	16.4748i	1.15655	−	1.30244i
$161$	−9.33209	+	9.33209i	−0.735472	+	0.735472i
$162$	0.0572703	−	1.41305i	0.00449958	−	0.111020i
$163$	−8.51519	−	14.7487i	−0.666961	−	1.15521i	−0.978750	−	0.205059i	$-0.934261\pi$
$163$	−8.51519	−	14.7487i	−0.666961	−	1.15521i	0.311789	−	0.950151i	$-0.399072\pi$
$164$	−5.88700	+	16.4945i	−0.459697	+	1.28801i
$165$	7.27712	+	1.94990i	0.566523	+	0.151799i
$166$	−7.23784	−	13.7983i	−0.561765	−	1.07095i
$167$	−3.94733	+	1.05768i	−0.305454	+	0.0818461i	−0.408290	−	0.912852i	$-0.633875\pi$
$167$	−3.94733	+	1.05768i	−0.305454	+	0.0818461i	0.102836	+	0.994698i	$0.467208\pi$
$168$	0.629472	−	5.15438i	0.0485648	−	0.397669i
$169$	12.8203	+	2.15432i	0.986173	+	0.165717i
$170$	3.02212	+	1.91205i	0.231786	+	0.146647i
$171$	−3.18616	+	5.51859i	−0.243652	+	0.422017i
$172$	−9.66642	+	8.21462i	−0.737058	+	0.626359i
$173$	−10.8065	−	2.89558i	−0.821600	−	0.220147i	−0.176554	−	0.984291i	$-0.556495\pi$
$173$	−10.8065	−	2.89558i	−0.821600	−	0.220147i	−0.645046	+	0.764144i	$0.723162\pi$
$174$	8.10343	+	5.12691i	0.614319	+	0.388670i
$175$	4.83232	−	18.0345i	0.365289	−	1.36328i
$176$	1.24818	−	7.63590i	0.0940851	−	0.575577i
$177$	−1.67418	−	1.67418i	−0.125839	−	0.125839i
$178$	−13.9972	−	15.1797i	−1.04913	−	1.13777i
$179$	−0.367172	+	0.0983834i	−0.0274437	+	0.00735352i	−0.272515	−	0.962152i	$-0.587855\pi$
$179$	−0.367172	+	0.0983834i	−0.0274437	+	0.00735352i	0.245071	+	0.969505i	$0.421189\pi$
$180$	−7.76414	−	0.630388i	−0.578705	−	0.0469864i
$181$	−9.11008	−	9.11008i	−0.677147	−	0.677147i	0.282207	−	0.959354i	$-0.408934\pi$
$181$	−9.11008	−	9.11008i	−0.677147	−	0.677147i	−0.959354	+	0.282207i	$0.908934\pi$
$182$	1.28821	+	9.27217i	0.0954887	+	0.687299i
$183$	−8.78118			−0.649123
$184$	12.2259	−	16.2463i	0.901304	−	1.19769i
$185$	1.87338	+	1.08160i	0.137734	+	0.0795206i
$186$	−0.0493739	+	1.21822i	−0.00362027	+	0.0893245i
$187$	1.25586			0.0918377
$188$	−1.02079	−	5.58481i	−0.0744490	−	0.407314i
$189$	−1.58993	+	0.917944i	−0.115650	+	0.0667706i
$190$	29.6615	+	18.7664i	2.15187	+	1.36146i
$191$	−8.20623	+	4.73787i	−0.593782	+	0.342820i	−0.766592	−	0.642135i	$-0.778049\pi$
$191$	−8.20623	+	4.73787i	−0.593782	+	0.342820i	0.172809	+	0.984955i	$0.444716\pi$
$192$	0.150036	+	7.99859i	0.0108279	+	0.577249i
$193$	3.06327	−	0.820802i	0.220499	−	0.0590826i	−0.146878	−	0.989155i	$-0.546922\pi$
$193$	3.06327	−	0.820802i	0.220499	−	0.0590826i	0.367377	+	0.930072i	$0.380256\pi$
$194$	−14.6846	+	3.30369i	−1.05429	+	0.237191i
$195$	13.8198	−	2.49418i	0.989656	−	0.178612i
$196$	6.55960	−	3.10887i	0.468543	−	0.222062i
$197$	−17.5918	−	10.1567i	−1.25337	−	0.723632i	−0.281590	−	0.959535i	$-0.590862\pi$
$197$	−17.5918	−	10.1567i	−1.25337	−	0.723632i	−0.971777	+	0.235903i	$0.924195\pi$
$198$	−2.42248	+	1.27070i	−0.172158	+	0.0903050i
$199$	15.0080	−	8.66488i	1.06389	−	0.614237i	0.137384	−	0.990518i	$-0.456131\pi$
$199$	15.0080	−	8.66488i	1.06389	−	0.614237i	0.926506	+	0.376281i	$0.122797\pi$
$200$	−3.48693	+	28.5524i	−0.246563	+	2.01896i
$201$	−3.40820	+	12.7196i	−0.240396	+	0.897170i
$202$	−7.06924	+	6.51854i	−0.497390	+	0.458643i
$203$		−	12.4483i		−	0.873698i
$204$	−1.27735	+	0.233474i	−0.0894323	+	0.0163465i
$205$	−8.82738	−	32.9442i	−0.616531	−	2.30092i
$206$	−2.98472	−	5.69009i	−0.207955	−	0.396447i
$207$	−7.18865			−0.499646
$208$	−3.96246	−	13.8672i	−0.274747	−	0.961516i
$209$	12.3260			0.852609
$210$	4.69737	+	8.95511i	0.324150	+	0.617961i
$211$	5.14114	+	19.1870i	0.353931	+	1.32089i	0.881825	+	0.471577i	$0.156315\pi$
$211$	5.14114	+	19.1870i	0.353931	+	1.32089i	−0.527894	+	0.849310i	$0.677018\pi$
$212$	1.82633	+	9.99192i	0.125433	+	0.686248i
$213$		−	12.0964i		−	0.828831i
$214$	12.6828	−	11.6948i	0.866977	−	0.799438i
$215$	6.39383	−	23.8621i	0.436055	−	1.62738i
$216$	2.22770	−	1.74280i	0.151576	−	0.118583i
$217$	1.37071	−	0.791379i	0.0930498	−	0.0537223i
$218$	−11.9811	+	6.28464i	−0.811462	+	0.425650i
$219$	0.862553	+	0.497995i	0.0582859	+	0.0336514i
$220$	6.45312	+	13.6159i	0.435069	+	0.917982i
$221$	2.11760	−	0.997847i	0.142445	−	0.0671224i
$222$	−0.766300	+	0.172400i	−0.0514307	+	0.0115707i
$223$	19.6911	−	5.27621i	1.31861	−	0.353321i	0.470155	−	0.882584i	$-0.344198\pi$
$223$	19.6911	−	5.27621i	1.31861	−	0.353321i	0.848458	+	0.529263i	$0.177531\pi$
$224$	8.67064	−	5.71626i	0.579332	−	0.381934i
$225$	8.80731	−	5.08491i	0.587154	−	0.338994i
$226$	20.4127	+	12.9148i	1.35783	+	0.859079i
$227$	19.4895	−	11.2522i	1.29356	−	0.746838i	0.314277	−	0.949331i	$-0.398238\pi$
$227$	19.4895	−	11.2522i	1.29356	−	0.746838i	0.979284	+	0.202493i	$0.0649045\pi$
$228$	−12.5369	+	2.29151i	−0.830278	+	0.151759i
$229$	0.593415			0.0392140			0.0196070	−	0.999808i	$-0.493759\pi$
$229$	0.593415			0.0392140			0.0196070	+	0.999808i	$0.493759\pi$
$230$	−1.60349	+	39.5636i	−0.105731	+	2.60875i
$231$	3.07541	+	1.77559i	0.202347	+	0.116825i
$232$	2.68145	+	18.9898i	0.176046	+	1.24674i
$233$	15.5368			1.01785			0.508926	−	0.860810i	$-0.330043\pi$
$233$	15.5368			1.01785			0.508926	+	0.860810i	$0.330043\pi$
$234$	−3.07508	+	4.06741i	−0.201025	+	0.265895i
$235$	7.81788	+	7.81788i	0.509982	+	0.509982i
$236$	0.383209	−	4.71977i	0.0249448	−	0.307231i
$237$	0.259863	−	0.0696301i	0.0168799	−	0.00452296i
$238$	1.14271	+	1.23925i	0.0740711	+	0.0803289i
$239$	−10.9950	−	10.9950i	−0.711206	−	0.711206i	0.255582	−	0.966787i	$-0.417733\pi$
$239$	−10.9950	−	10.9950i	−0.711206	−	0.711206i	−0.966787	+	0.255582i	$0.917733\pi$
$240$	−9.09483	−	12.6492i	−0.587069	−	0.816499i
$241$	−4.22835	+	15.7804i	−0.272372	+	1.01650i	0.685211	+	0.728345i	$0.259710\pi$
$241$	−4.22835	+	15.7804i	−0.272372	+	1.01650i	−0.957582	+	0.288160i	$0.906957\pi$
$242$	−8.67461	−	5.48829i	−0.557625	−	0.352800i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	−11.3728	−	13.3827i	−0.728066	−	0.856740i
$245$	−7.06819	+	12.2425i	−0.451570	+	0.782142i
$246$	10.4653	+	6.62123i	0.667243	+	0.422154i
$247$	20.7838	−	9.79367i	1.32244	−	0.623156i
$248$	−1.92054	+	1.50251i	−0.121955	+	0.0954094i
$249$	−10.6423	+	2.85159i	−0.674426	+	0.180712i
$250$	−13.2277	−	25.2173i	−0.836591	−	1.59488i
$251$	−8.51783	−	2.28235i	−0.537641	−	0.144060i	−0.0202263	−	0.999795i	$-0.506439\pi$
$251$	−8.51783	−	2.28235i	−0.537641	−	0.144060i	−0.517414	+	0.855735i	$0.673105\pi$
$252$	−3.45813	−	1.23423i	−0.217841	−	0.0777490i
$253$	6.95254	+	12.0422i	0.437102	+	0.757084i
$254$	0.00830694	−	0.204961i	0.000521224	−	0.0128604i
$255$	1.78810	−	1.78810i	0.111975	−	0.111975i
$256$	−11.9957	+	10.5879i	−0.749732	+	0.661741i
$257$	1.43378	+	0.827794i	0.0894368	+	0.0516363i	0.544051	−	0.839052i	$-0.316890\pi$
$257$	1.43378	+	0.827794i	0.0894368	+	0.0516363i	−0.454615	+	0.890688i	$0.650223\pi$
$258$	4.16671	+	7.94345i	0.259408	+	0.494538i
$259$	0.721003	+	0.721003i	0.0448009	+	0.0448009i
$260$	21.6996	+	17.8314i	1.34575	+	1.10585i
$261$	4.79455	−	4.79455i	0.296775	−	0.296775i
$262$	−8.55407	+	27.4287i	−0.528472	+	1.69455i
$263$	−8.03994	+	13.9256i	−0.495764	+	0.858688i	−0.999988	−	0.00488454i	$-0.998445\pi$
$263$	−8.03994	+	13.9256i	−0.495764	+	0.858688i	0.504224	+	0.863573i	$0.331779\pi$
$264$	−5.07401	−	2.04619i	−0.312283	−	0.125934i
$265$	−13.9872	−	13.9872i	−0.859226	−	0.859226i
$266$	11.2155	+	12.1630i	0.687667	+	0.745763i
$267$	−12.6443	+	7.30020i	−0.773820	+	0.446765i
$268$	−23.7990	+	11.2793i	−1.45375	+	0.688994i
$269$	−5.29387	+	19.7570i	−0.322773	+	1.20461i	0.593759	+	0.804643i	$0.297643\pi$
$269$	−5.29387	+	19.7570i	−0.322773	+	1.20461i	−0.916532	+	0.399962i	$0.869023\pi$
$270$	−1.63990	+	5.25836i	−0.0998012	+	0.320014i
$271$	−0.00815071	−	0.0304188i	−0.000495120	−	0.00184781i	0.965678	−	0.259743i	$-0.0836378\pi$
$271$	−0.00815071	−	0.0304188i	−0.000495120	−	0.00184781i	−0.966173	+	0.257895i	$0.916971\pi$
$272$	−2.01015	−	1.64433i	−0.121883	−	0.0997021i
$273$	6.59647	+	0.550379i	0.399237	+	0.0333104i
$274$	30.5772	−	6.87915i	1.84724	−	0.415585i
$275$	−17.0361	−	9.83578i	−1.02731	−	0.593120i
$276$	−9.31023	−	10.9557i	−0.560410	−	0.659453i
$277$	2.86602	−	10.6961i	0.172203	−	0.642669i	−0.824809	−	0.565412i	$-0.808717\pi$
$277$	2.86602	−	10.6961i	0.172203	−	0.642669i	0.997011	−	0.0772568i	$-0.0246161\pi$
$278$	0.540007	+	2.40028i	0.0323875	+	0.143959i
$279$	0.832745	+	0.223133i	0.0498551	+	0.0133586i
$280$	−7.56408	+	18.7569i	−0.452040	+	1.12094i
$281$	−17.3619	+	17.3619i	−1.03572	+	1.03572i	−0.0363861	+	0.999338i	$0.511585\pi$
$281$	−17.3619	+	17.3619i	−1.03572	+	1.03572i	−0.999338	+	0.0363861i	$0.988415\pi$
$282$	−4.01118	−	0.162571i	−0.238863	−	0.00968097i
$283$	−5.28953	−	19.7408i	−0.314430	−	1.17347i	−0.924519	−	0.381136i	$-0.875533\pi$
$283$	−5.28953	−	19.7408i	−0.314430	−	1.17347i	0.610089	−	0.792333i	$-0.291134\pi$
$284$	18.4352	−	15.6664i	1.09393	−	0.929628i
$285$	17.5498	−	17.5498i	1.03956	−	1.03956i
$286$	9.78766	+	1.21744i	0.578756	+	0.0719888i
$287$		−	16.0765i		−	0.948967i
$288$	5.54123	+	1.13790i	0.326520	+	0.0670515i
$289$	−8.28923	+	14.3574i	−0.487602	+	0.844551i
$290$	−25.3179	−	27.4569i	−1.48672	−	1.61232i
$291$			10.6431i			0.623911i
$292$	0.358161	+	1.95952i	0.0209598	+	0.114672i
$293$	8.54381	+	14.7983i	0.499135	+	0.864526i	1.00000		0.000998996i	$-0.000317990\pi$
$293$	8.54381	+	14.7983i	0.499135	+	0.864526i	−0.500865	+	0.865525i	$0.666985\pi$
$294$	−1.12662	−	5.00774i	−0.0657060	−	0.292057i
$295$	4.61081	+	7.98616i	0.268452	+	0.464972i
$296$	−1.25520	−	0.944579i	−0.0729569	−	0.0549025i
$297$	0.500636	+	1.86840i	0.0290499	+	0.108416i
$298$	13.3713	−	21.1343i	0.774580	−	1.22428i
$299$	21.2913	+	14.7810i	1.23131	+	0.854808i
$300$	19.1561	+	6.83693i	1.10598	+	0.394731i
$301$	5.82225	−	10.0844i	0.335589	−	0.581257i
$302$	−4.13011	−	1.28804i	−0.237661	−	0.0741182i
$303$	3.39973	+	5.88851i	0.195310	+	0.338286i
$304$	−19.7292	−	16.1388i	−1.13155	−	0.925621i
$305$	33.0359	+	8.85195i	1.89163	+	0.506861i
$306$	−0.0371831	+	0.917433i	−0.00212561	+	0.0524462i
$307$	−1.35874			−0.0775471			−0.0387736	−	0.999248i	$-0.512345\pi$
$307$	−1.35874			−0.0775471			−0.0387736	+	0.999248i	$0.512345\pi$
$308$	1.27702	+	6.98661i	0.0727647	+	0.398099i
$309$	−4.38862	+	1.17593i	−0.249660	+	0.0668962i
$310$	1.41379	−	4.53334i	0.0802980	−	0.257477i
$311$		−	20.8877i		−	1.18443i	−0.805779	−	0.592216i	$-0.798253\pi$
$311$		−	20.8877i		−	1.18443i	0.805779	−	0.592216i	$-0.201747\pi$
$312$	−10.1815	+	0.581330i	−0.576411	+	0.0329113i
$313$		−	15.7754i		−	0.891680i	−0.895113	−	0.445840i	$-0.852905\pi$
$313$		−	15.7754i		−	0.891680i	0.895113	−	0.445840i	$-0.147095\pi$
$314$	−2.82979	−	0.882514i	−0.159694	−	0.0498031i
$315$	6.90685	−	1.85069i	0.389157	−	0.104274i
$316$	0.442674	+	0.305857i	0.0249024	+	0.0172058i
$317$	12.3594			0.694173			0.347087	−	0.937833i	$-0.387171\pi$
$317$	12.3594			0.694173			0.347087	+	0.937833i	$0.387171\pi$
$318$	7.17652	+	0.290860i	0.402439	+	0.0163106i
$319$	−12.6687	−	3.39457i	−0.709312	−	0.190060i
$320$	7.49861	−	30.2430i	0.419185	−	1.69063i
$321$	−6.09939	−	10.5645i	−0.340435	−	0.589651i
$322$	−5.55676	+	17.8178i	−0.309666	+	0.992947i
$323$	2.06863	−	3.58297i	0.115102	−	0.199362i
$324$	−0.856552	−	1.80730i	−0.0475862	−	0.100405i
$325$	−36.5408	−	3.04879i	−2.02692	−	0.169117i
$326$	−20.3531	−	12.8771i	−1.12725	−	0.713195i
$327$	2.47604	+	9.24072i	0.136926	+	0.511013i
$328$	3.46301	+	24.5247i	0.191212	+	1.35415i
$329$	2.60574	+	4.51327i	0.143659	+	0.248825i
$330$	10.3946	−	2.33855i	0.572206	−	0.128733i
$331$	−10.1029	−	17.4987i	−0.555304	−	0.961816i	−0.997880	−	0.0650842i	$-0.979268\pi$
$331$	−10.1029	−	17.4987i	−0.555304	−	0.961816i	0.442575	−	0.896731i	$-0.354065\pi$
$332$	−18.1290	−	12.5259i	−0.994958	−	0.687447i
$333$			0.555400i			0.0304357i
$334$	−4.24872	+	3.91774i	−0.232479	+	0.214369i
$335$	25.6442	−	44.4170i	1.40109	−	2.42676i
$336$	−2.59773	−	6.86874i	−0.141718	−	0.374721i
$337$			17.5473i			0.955861i	0.878398	+	0.477930i	$0.158613\pi$
$337$			17.5473i			0.955861i	−0.878398	+	0.477930i	$0.841387\pi$
$338$	17.4710	−	5.72398i	0.950297	−	0.311343i
$339$	12.0776	−	12.0776i	0.655963	−	0.655963i
$340$	5.04091	+	0.409283i	0.273382	+	0.0221965i
$341$	−0.431609	−	1.61079i	−0.0233729	−	0.0872290i
$342$	−0.364944	+	9.00442i	−0.0197339	+	0.486903i
$343$	−13.7989	+	13.7989i	−0.745071	+	0.745071i
$344$	−6.70957	+	16.6379i	−0.361756	+	0.897058i
$345$	27.0447	+	7.24659i	1.45604	+	0.390143i
$346$	−15.4359	+	3.47272i	−0.829841	+	0.186695i
$347$	−0.833621	+	3.11111i	−0.0447511	+	0.167013i	−0.984685	−	0.174343i	$-0.944220\pi$
$347$	−0.833621	+	3.11111i	−0.0447511	+	0.167013i	0.939934	+	0.341357i	$0.110886\pi$
$348$	13.5166	+	1.09744i	0.724563	+	0.0588290i
$349$	26.9565	+	15.5634i	1.44295	+	0.833088i	0.998046	−	0.0624905i	$-0.0199043\pi$
$349$	26.9565	+	15.5634i	1.44295	+	0.833088i	0.444904	+	0.895578i	$0.353238\pi$
$350$	−5.79548	−	25.7604i	−0.309782	−	1.37695i
$351$	2.32870	+	2.75266i	0.124297	+	0.146926i
$352$	−3.45305	−	10.3830i	−0.184048	−	0.553414i
$353$	−1.86315	−	6.95338i	−0.0991656	−	0.370091i	0.898452	−	0.439071i	$-0.144692\pi$
$353$	−1.86315	−	6.95338i	−0.0991656	−	0.370091i	−0.997618	+	0.0689798i	$0.978026\pi$
$354$	−3.19652	−	0.996884i	−0.169893	−	0.0529838i
$355$	−12.1939	+	45.5082i	−0.647184	+	2.41532i
$356$	−27.5017	−	9.81552i	−1.45759	−	0.520221i
$357$	1.03227	−	0.595981i	0.0546335	−	0.0315426i
$358$	−0.395206	+	0.364419i	−0.0208873	+	0.0192601i
$359$	7.91634	+	7.91634i	0.417809	+	0.417809i	0.884448	−	0.466639i	$-0.154535\pi$
$359$	7.91634	+	7.91634i	0.417809	+	0.417809i	−0.466639	+	0.884448i	$0.654535\pi$
$360$	−10.1377	+	4.31101i	−0.534306	+	0.227210i
$361$	10.8032	−	18.7117i	0.568590	−	0.984826i
$362$	−17.3939	−	5.42456i	−0.914204	−	0.285109i
$363$	−5.13250	+	5.13250i	−0.269386	+	0.269386i
$364$	7.70449	+	10.7660i	0.403825	+	0.564291i
$365$	−2.74303	−	2.74303i	−0.143577	−	0.143577i
$366$	−10.9973	+	5.76861i	−0.574840	+	0.301530i
$367$	14.5787	+	8.41699i	0.760999	+	0.439363i	0.829654	−	0.558277i	$-0.188537\pi$
$367$	14.5787	+	8.41699i	0.760999	+	0.439363i	−0.0686550	+	0.997640i	$0.521871\pi$
$368$	4.63873	−	28.3780i	0.241810	−	1.47930i
$369$	6.19199	−	6.19199i	0.322342	−	0.322342i
$370$	3.05671	+	0.123887i	0.158911	+	0.00644057i
$371$	−4.66199	−	8.07481i	−0.242039	−	0.419223i
$372$	0.738452	+	1.55811i	0.0382869	+	0.0807841i
$373$	−0.0971765	−	0.0260384i	−0.00503161	−	0.00134822i	0.256302	−	0.966597i	$-0.417496\pi$
$373$	−0.0971765	−	0.0260384i	−0.00503161	−	0.00134822i	−0.261334	+	0.965248i	$0.584162\pi$
$374$	1.57281	−	0.825012i	0.0813281	−	0.0426604i
$375$	−19.4495	+	5.21148i	−1.00437	+	0.269120i
$376$	−4.94724	−	6.32368i	−0.255134	−	0.326119i
$377$	−24.0588	+	4.34211i	−1.23909	+	0.223630i
$378$	−1.38816	+	2.19408i	−0.0713993	+	0.112851i
$379$	7.53912	−	13.0581i	0.387259	−	0.670751i	−0.604821	−	0.796361i	$-0.706755\pi$
$379$	7.53912	−	13.0581i	0.387259	−	0.670751i	0.992080	+	0.125610i	$0.0400888\pi$
$380$	49.4755	+	4.01703i	2.53804	+	0.206069i
$381$	−0.140106	−	0.0375412i	−0.00717783	−	0.00192329i
$382$	−7.16484	+	11.3245i	−0.366585	+	0.579412i
$383$	−0.605828	+	2.26098i	−0.0309563	+	0.115531i	−0.979675	−	0.200590i	$-0.935714\pi$
$383$	−0.605828	+	2.26098i	−0.0309563	+	0.115531i	0.948719	+	0.316121i	$0.102381\pi$
$384$	5.44241	+	9.91868i	0.277732	+	0.506160i
$385$	−9.78019	−	9.78019i	−0.498445	−	0.498445i
$386$	3.29716	−	3.04031i	0.167821	−	0.154747i
$387$	6.12658	−	1.64161i	0.311432	−	0.0834479i
$388$	−16.2203	+	13.7842i	−0.823463	+	0.699787i
$389$	3.27429	+	3.27429i	0.166013	+	0.166013i	0.785225	−	0.619211i	$-0.212548\pi$
$389$	3.27429	+	3.27429i	0.166013	+	0.166013i	−0.619211	+	0.785225i	$0.712548\pi$
$390$	15.6691	−	12.2023i	0.793434	−	0.617886i
$391$	4.66727			0.236034
$392$	6.17278	−	8.20266i	0.311772	−	0.414297i
$393$	17.5945	+	10.1582i	0.887523	+	0.512412i
$394$	−28.7038	−	1.16335i	−1.44608	−	0.0586087i
$395$	−1.04783			−0.0527221
$396$	−2.19909	+	3.18280i	−0.110509	+	0.159942i
$397$	−0.961472	+	0.555106i	−0.0482549	+	0.0278600i	−0.523933	−	0.851759i	$-0.675536\pi$
$397$	−0.961472	+	0.555106i	−0.0482549	+	0.0278600i	0.475678	+	0.879619i	$0.342203\pi$
$398$	13.1034	−	20.7109i	0.656817	−	1.03814i
$399$	10.1315	−	5.84943i	0.507210	−	0.292838i
$400$	14.3900	+	38.0490i	0.719499	+	1.90245i
$401$	10.0958	−	2.70517i	0.504161	−	0.135090i	0.00223048	−	0.999998i	$-0.499290\pi$
$401$	10.0958	−	2.70517i	0.504161	−	0.135090i	0.501930	+	0.864908i	$0.332623\pi$
$402$	4.08752	+	18.1686i	0.203867	+	0.906169i
$403$	−2.00762	−	2.37313i	−0.100007	−	0.118214i
$404$	−4.57113	+	12.8076i	−0.227422	+	0.637204i
$405$	3.37303	+	1.94742i	0.167607	+	0.0967682i
$406$	−8.17764	−	15.5899i	−0.405849	−	0.773714i
$407$	0.930384	−	0.537157i	0.0461174	−	0.0266259i
$408$	−1.44634	+	1.13153i	−0.0716047	+	0.0560189i
$409$	−7.75749	+	28.9514i	−0.383583	+	1.43155i	0.456805	+	0.889567i	$0.348994\pi$
$409$	−7.75749	+	28.9514i	−0.383583	+	1.43155i	−0.840388	+	0.541985i	$0.817673\pi$
$410$	−32.6972	−	35.4596i	−1.61480	−	1.75122i
$411$		−	22.1618i		−	1.09316i
$412$	−7.47597	−	5.16538i	−0.368314	−	0.254480i
$413$	1.12502	+	4.19863i	0.0553586	+	0.206601i
$414$	−9.00289	+	4.72244i	−0.442468	+	0.232095i
$415$	42.9122			2.10648
$416$	−14.0723	−	14.7639i	−0.689949	−	0.723858i
$417$	1.73968			0.0851924
$418$	15.4368	−	8.09733i	0.755039	−	0.396053i
$419$	−3.33343	−	12.4405i	−0.162849	−	0.607760i	−0.998305	−	0.0582025i	$-0.981463\pi$
$419$	−3.33343	−	12.4405i	−0.162849	−	0.607760i	0.835456	−	0.549557i	$-0.185204\pi$
$420$	11.7657	+	8.12932i	0.574110	+	0.396670i
$421$			29.6181i			1.44350i	0.692156	+	0.721748i	$0.256661\pi$
$421$			29.6181i			1.44350i	−0.692156	+	0.721748i	$0.743339\pi$
$422$	19.0431	+	20.6520i	0.927005	+	1.00532i
$423$	−0.734700	+	2.74194i	−0.0357224	+	0.133318i
$424$	8.85123	+	11.3139i	0.429854	+	0.549450i
$425$	−5.71820	+	3.30140i	−0.277373	+	0.160142i
$426$	−7.94647	−	15.1492i	−0.385008	−	0.733982i
$427$	13.9614	+	8.06063i	0.675641	+	0.390081i
$428$	8.20097	−	22.9779i	0.396409	−	1.11068i
$429$	2.35894	−	6.56320i	0.113891	−	0.316874i
$430$	−7.66823	−	34.0846i	−0.369795	−	1.64370i
$431$	−27.8486	+	7.46202i	−1.34142	+	0.359433i	−0.856961	−	0.515381i	$-0.827651\pi$
$431$	−27.8486	+	7.46202i	−1.34142	+	0.359433i	−0.484460	+	0.874813i	$0.660984\pi$
$432$	1.64501	−	3.64608i	0.0791457	−	0.175422i
$433$	6.19249	−	3.57523i	0.297592	−	0.171815i	−0.343769	−	0.939054i	$-0.611704\pi$
$433$	6.19249	−	3.57523i	0.297592	−	0.171815i	0.641361	+	0.767240i	$0.278370\pi$
$434$	1.19676	−	1.89156i	0.0574464	−	0.0907979i
$435$	−22.8709	+	13.2045i	−1.09658	+	0.633109i
$436$	−10.8763	+	15.7415i	−0.520879	+	0.753880i
$437$	45.8084			2.19131
$438$	1.40739	+	0.0570407i	0.0672476	+	0.00272551i
$439$	19.6285	+	11.3325i	0.936818	+	0.540872i	0.888961	−	0.457982i	$-0.151428\pi$
$439$	19.6285	+	11.3325i	0.936818	+	0.540872i	0.0478567	+	0.998854i	$0.484761\pi$
$440$	17.0264	+	12.8129i	0.811701	+	0.610833i
$441$	−3.62951			−0.172834
$442$	1.99652	−	2.64079i	0.0949646	−	0.125610i
$443$	−1.78307	−	1.78307i	−0.0847164	−	0.0847164i	0.663479	−	0.748195i	$-0.269079\pi$
$443$	−1.78307	−	1.78307i	−0.0847164	−	0.0847164i	−0.748195	+	0.663479i	$0.769079\pi$
$444$	−0.846441	+	0.719314i	−0.0401703	+	0.0341371i
$445$	54.9286	−	14.7181i	2.60387	−	0.697704i
$446$	21.1945	−	19.5434i	1.00359	−	0.925409i
$447$	−12.5045	−	12.5045i	−0.591442	−	0.591442i
$448$	7.10372	−	12.8549i	0.335619	−	0.607337i
$449$	−8.83990	+	32.9910i	−0.417181	+	1.55694i	0.363247	+	0.931693i	$0.381668\pi$
$449$	−8.83990	+	32.9910i	−0.417181	+	1.55694i	−0.780427	+	0.625247i	$0.784998\pi$
$450$	7.68964	−	12.1540i	0.362493	−	0.572945i
$451$	−16.3612	−	4.38397i	−0.770419	−	0.206433i
$452$	34.0484	+	2.76447i	1.60150	+	0.130030i
$453$	−1.52958	+	2.64930i	−0.0718657	+	0.124475i
$454$	17.0162	−	26.8952i	0.798609	−	1.26226i
$455$	−24.2620	−	8.72023i	−1.13742	−	0.408811i
$456$	−14.1956	+	11.1057i	−0.664769	+	0.520072i
$457$	5.39298	−	1.44504i	0.252273	−	0.0675963i	−0.130466	−	0.991453i	$-0.541647\pi$
$457$	5.39298	−	1.44504i	0.252273	−	0.0675963i	0.382739	+	0.923856i	$0.374981\pi$
$458$	0.743178	−	0.389832i	0.0347264	−	0.0182156i
$459$	0.627133	+	0.168040i	0.0292721	+	0.00784342i
$460$	23.9823	+	50.6019i	1.11818	+	2.35933i
$461$	−10.9669	−	18.9952i	−0.510777	−	0.884693i	−0.999922	−	0.0124898i	$-0.996024\pi$
$461$	−10.9669	−	18.9952i	−0.510777	−	0.884693i	0.489145	−	0.872203i	$-0.337309\pi$
$462$	5.01800	+	0.203377i	0.233459	+	0.00946196i
$463$	−20.5243	+	20.5243i	−0.953844	+	0.953844i	−0.998981	−	0.0451368i	$-0.985628\pi$
$463$	−20.5243	+	20.5243i	−0.953844	+	0.953844i	0.0451368	+	0.998981i	$0.485628\pi$
$464$	15.8332	+	22.0208i	0.735036	+	1.02229i
$465$	−2.90796	−	1.67891i	−0.134854	−	0.0778578i
$466$	19.4579	−	10.2066i	0.901372	−	0.472811i
$467$	−24.4589	−	24.4589i	−1.13182	−	1.13182i	−0.989874	−	0.141949i	$-0.954663\pi$
$467$	−24.4589	−	24.4589i	−1.13182	−	1.13182i	−0.141949	−	0.989874i	$-0.545337\pi$
$468$	−1.17916	+	7.11404i	−0.0545065	+	0.328847i
$469$	17.0947	−	17.0947i	0.789358	−	0.789358i
$470$	14.9267	+	4.65513i	0.688518	+	0.214725i
$471$	−1.04801	+	1.81520i	−0.0482896	+	0.0836401i
$472$	−2.62063	−	6.16266i	−0.120624	−	0.283659i
$473$	−8.67532	−	8.67532i	−0.398892	−	0.398892i
$474$	0.279704	−	0.257915i	0.0128472	−	0.0118464i
$475$	−56.1230	+	32.4026i	−2.57510	+	1.48673i
$476$	2.24521	+	0.801329i	0.102909	+	0.0367288i
$477$	1.31447	−	4.90568i	0.0601855	−	0.224616i
$478$	−20.9927	−	6.54691i	−0.960186	−	0.299449i
$479$	9.15092	+	34.1517i	0.418116	+	1.56043i	0.778511	+	0.627631i	$0.215975\pi$
$479$	9.15092	+	34.1517i	0.418116	+	1.56043i	−0.360395	+	0.932800i	$0.617358\pi$
$480$	−19.6997	−	9.86682i	−0.899166	−	0.450357i
$481$	1.14199	−	1.64498i	0.0520702	−	0.0750046i
$482$	5.07113	+	22.5407i	0.230984	+	1.02670i
$483$	11.4294	+	6.59878i	0.520057	+	0.300255i
$484$	−14.4693	−	1.17479i	−0.657695	−	0.0533997i
$485$	10.7289	−	40.0408i	0.487174	−	1.81816i
$486$	−1.37973	+	0.310406i	−0.0625857	+	0.0140803i
$487$	6.73792	+	1.80542i	0.305324	+	0.0818114i	0.408228	−	0.912880i	$-0.366147\pi$
$487$	6.73792	+	1.80542i	0.305324	+	0.0818114i	−0.102904	+	0.994691i	$0.532813\pi$
$488$	−23.0344	−	9.28908i	−1.04272	−	0.420497i
$489$	−12.0423	+	12.0423i	−0.544571	+	0.544571i
$490$	−0.809595	+	19.9755i	−0.0365738	+	0.902399i
$491$	−0.134595	−	0.502315i	−0.00607419	−	0.0226692i	0.962822	−	0.270136i	$-0.0870686\pi$
$491$	−0.134595	−	0.502315i	−0.00607419	−	0.0226692i	−0.968896	+	0.247467i	$0.920402\pi$
$492$	17.4562	+	1.41731i	0.786984	+	0.0638971i
$493$	−3.11289	+	3.11289i	−0.140197	+	0.140197i
$494$	19.5954	−	25.9188i	0.881639	−	1.16614i
$495$		−	7.53383i		−	0.338621i
$496$	−1.41820	+	3.14337i	−0.0636791	+	0.141141i
$497$	−11.1038	+	19.2324i	−0.498074	+	0.862689i
$498$	−11.4548	+	10.5625i	−0.513303	+	0.473316i
$499$		−	37.2078i		−	1.66565i	−0.553536	−	0.832825i	$-0.686722\pi$
$499$		−	37.2078i		−	1.66565i	0.553536	−	0.832825i	$-0.313278\pi$
$500$	−33.1320	−	22.8919i	−1.48171	−	1.02376i
$501$	2.04329	+	3.53908i	0.0912874	+	0.158114i
$502$	−12.1669	+	2.73726i	−0.543033	+	0.122170i
$503$	−5.55866	−	9.62788i	−0.247848	−	0.429286i	0.715080	−	0.699042i	$-0.246390\pi$
$503$	−5.55866	−	9.62788i	−0.247848	−	0.429286i	−0.962929	+	0.269756i	$0.913057\pi$
$504$	−5.14167	+	0.726029i	−0.229028	+	0.0323399i
$505$	−6.85427	−	25.5805i	−0.305011	−	1.13832i
$506$	16.6180	+	10.5140i	0.738762	+	0.467403i
$507$	−1.23721	−	12.9410i	−0.0549465	−	0.574730i
$508$	−0.124241	−	0.262145i	−0.00551231	−	0.0116308i
$509$	0.719605	−	1.24639i	0.0318960	−	0.0552454i	−0.849637	−	0.527368i	$-0.823179\pi$
$509$	0.719605	−	1.24639i	0.0318960	−	0.0552454i	0.881533	+	0.472123i	$0.156512\pi$
$510$	1.06471	−	3.41402i	0.0471464	−	0.151175i
$511$	−0.914264	−	1.58355i	−0.0404447	−	0.0700522i
$512$	−8.06766	+	21.1403i	−0.356544	+	0.934279i
$513$	6.15518	+	1.64928i	0.271758	+	0.0728173i
$514$	2.33943	+	0.0948160i	0.103188	+	0.00418215i
$515$	17.6960			0.779778
$516$	10.4366	+	7.21095i	0.459444	+	0.317444i
$517$	5.30376	−	1.42114i	0.233259	−	0.0625016i
$518$	1.37661	+	0.429318i	0.0604850	+	0.0188632i
$519$			11.1877i			0.491084i
$520$	38.8900	+	8.07648i	1.70544	+	0.354177i
$521$			36.2767i			1.58931i	0.607059	+	0.794656i	$0.292349\pi$
$521$			36.2767i			1.58931i	−0.607059	+	0.794656i	$0.707651\pi$
$522$	2.85490	−	9.15425i	0.124955	−	0.400671i
$523$	23.9887	−	6.42775i	1.04895	−	0.281066i	0.307133	−	0.951667i	$-0.400630\pi$
$523$	23.9887	−	6.42775i	1.04895	−	0.281066i	0.741818	+	0.670601i	$0.233964\pi$
$524$	7.30582	+	39.9705i	0.319156	+	1.74612i
$525$	−18.6706			−0.814854
$526$	−0.920900	+	22.7217i	−0.0401531	+	0.990714i
$527$	−0.540664	−	0.144871i	−0.0235517	−	0.00631066i
$528$	−7.69876	+	0.770666i	−0.335046	+	0.0335389i
$529$	14.3384	+	24.8348i	0.623407	+	1.07977i
$530$	−26.7058	−	8.32861i	−1.16003	−	0.361772i
$531$	−1.18382	+	2.05044i	−0.0513736	+	0.0889817i
$532$	22.0363	+	7.86488i	0.955394	+	0.340986i
$533$	−31.0711	+	5.60768i	−1.34584	+	0.242896i
$534$	−11.0397	+	17.4490i	−0.477735	+	0.755092i
$535$	12.2971	+	45.8934i	0.531650	+	1.98415i
$536$	−22.3955	+	29.7602i	−0.967340	+	1.28544i
$537$	0.190062	+	0.329197i	0.00820178	+	0.0142059i
$538$	6.34904	+	28.2209i	0.273726	+	1.21669i
$539$	3.51030	+	6.08002i	0.151199	+	0.261885i
$540$	1.40060	+	7.66274i	0.0602722	+	0.329752i
$541$			18.4244i			0.792128i	0.918223	+	0.396064i	$0.129624\pi$
$541$			18.4244i			0.792128i	−0.918223	+	0.396064i	$0.870376\pi$
$542$	−0.0301908	−	0.0327414i	−0.00129680	−	0.00140636i
$543$	−6.44180	+	11.1575i	−0.276444	+	0.478815i
$544$	−3.59767	−	0.738790i	−0.154249	−	0.0316753i
$545$		−	37.2608i		−	1.59608i
$546$	8.62282	−	3.64413i	0.369023	−	0.155955i
$547$	−5.05841	+	5.05841i	−0.216282	+	0.216282i	−0.806930	−	0.590648i	$-0.798872\pi$
$547$	−5.05841	+	5.05841i	−0.216282	+	0.216282i	0.590648	+	0.806930i	$0.298872\pi$
$548$	33.7750	−	28.7023i	1.44280	−	1.22610i
$549$	2.27274	+	8.48197i	0.0969980	+	0.362001i
$550$	−27.7970	−	1.12660i	−1.18527	−	0.0480382i
$551$	−30.5524	+	30.5524i	−1.30158	+	1.30158i
$552$	−18.8570	−	7.60444i	−0.802607	−	0.323667i
$553$	−0.477080	−	0.127833i	−0.0202875	−	0.00543602i
$554$	−3.43727	−	15.2784i	−0.146036	−	0.649115i
$555$	0.559876	−	2.08949i	0.0237654	−	0.0886937i
$556$	2.25311	+	2.65131i	0.0955530	+	0.112440i
$557$	−22.6961	−	13.1036i	−0.961666	−	0.555218i	−0.0649805	−	0.997887i	$-0.520699\pi$
$557$	−22.6961	−	13.1036i	−0.961666	−	0.555218i	−0.896685	+	0.442668i	$0.854032\pi$
$558$	1.18949	−	0.267608i	0.0503552	−	0.0113287i
$559$	−21.5211	−	7.73511i	−0.910245	−	0.327160i
$560$	2.84890	+	28.4598i	0.120388	+	1.20264i
$561$	−0.325041	−	1.21307i	−0.0137232	−	0.0512158i
$562$	−10.3381	+	33.1491i	−0.436085	+	1.39831i
$563$	−4.98881	+	18.6185i	−0.210253	+	0.784676i	0.777530	+	0.628845i	$0.216472\pi$
$563$	−4.98881	+	18.6185i	−0.210253	+	0.784676i	−0.987784	+	0.155831i	$0.950195\pi$
$564$	−5.13031	+	2.43146i	−0.216025	+	0.102383i
$565$	−57.6122	+	33.2624i	−2.42376	+	1.39936i
$566$	−19.5928	−	21.2480i	−0.823546	−	0.893122i
$567$	1.29817	+	1.29817i	0.0545180	+	0.0545180i
$568$	12.7960	−	31.7308i	0.536910	−	1.33139i
$569$	2.04693	−	3.54539i	0.0858117	−	0.148630i	−0.819925	−	0.572471i	$-0.805985\pi$
$569$	2.04693	−	3.54539i	0.0858117	−	0.148630i	0.905737	+	0.423841i	$0.139318\pi$
$570$	10.4500	−	33.5079i	0.437701	−	1.40349i
$571$	−12.2352	+	12.2352i	−0.512026	+	0.512026i	−0.915147	−	0.403121i	$-0.867925\pi$
$571$	−12.2352	+	12.2352i	−0.512026	+	0.512026i	0.403121	+	0.915147i	$0.367925\pi$
$572$	13.0576	−	4.90510i	0.545965	−	0.205093i
$573$	6.70036	+	6.70036i	0.279912	+	0.279912i
$574$	−10.5611	−	20.1338i	−0.440813	−	0.840370i
$575$	−63.3127	−	36.5536i	−2.64032	−	1.52439i
$576$	7.68722	−	2.21511i	0.320301	−	0.0922963i
$577$	31.1267	−	31.1267i	1.29582	−	1.29582i	0.364696	−	0.931127i	$-0.381173\pi$
$577$	31.1267	−	31.1267i	1.29582	−	1.29582i	0.931127	−	0.364696i	$-0.118827\pi$
$578$	−0.949454	+	23.4263i	−0.0394921	+	0.974404i
$579$	−1.58567	−	2.74646i	−0.0658981	−	0.114139i
$580$	−49.7448	−	17.7542i	−2.06554	−	0.737203i
$581$	19.5380	+	5.23520i	0.810574	+	0.217193i
$582$	6.99177	+	13.3292i	0.289818	+	0.552512i
$583$	−9.48910	+	2.54260i	−0.392998	+	0.105304i
$584$	1.73582	+	2.21876i	0.0718286	+	0.0918131i
$585$	−5.98602	−	12.7034i	−0.247491	−	0.525219i
$586$	20.4215	+	12.9204i	0.843604	+	0.533735i
$587$	8.96067	−	15.5203i	0.369846	−	0.640593i	−0.619695	−	0.784843i	$-0.712744\pi$
$587$	8.96067	−	15.5203i	0.369846	−	0.640593i	0.989541	+	0.144250i	$0.0460770\pi$
$588$	−4.70068	−	5.53145i	−0.193853	−	0.228113i
$589$	−5.30651	−	1.42188i	−0.218651	−	0.0585874i
$590$	11.0208	+	6.97269i	0.453720	+	0.287061i
$591$	−5.25747	+	19.6212i	−0.216263	+	0.807106i
$592$	−2.19250	−	0.358391i	−0.0901112	−	0.0147298i
$593$	−33.9153	−	33.9153i	−1.39273	−	1.39273i	−0.819142	−	0.573590i	$-0.805550\pi$
$593$	−33.9153	−	33.9153i	−1.39273	−	1.39273i	−0.573590	−	0.819142i	$-0.694450\pi$
$594$	1.85439	+	2.01106i	0.0760866	+	0.0825146i
$595$	−4.48431	+	1.20157i	−0.183839	+	0.0492595i
$596$	2.86220	−	35.2520i	0.117240	−	1.44398i
$597$	−12.2540	−	12.2540i	−0.501522	−	0.501522i
$598$	36.3748	+	4.52449i	1.48748	+	0.185020i
$599$	−5.69780			−0.232806			−0.116403	−	0.993202i	$-0.537136\pi$
$599$	−5.69780			−0.232806			−0.116403	+	0.993202i	$0.537136\pi$
$600$	28.4820	−	4.02180i	1.16277	−	0.164189i
$601$	−35.0789	−	20.2528i	−1.43090	−	0.826130i	−0.433710	−	0.901052i	$-0.642796\pi$
$601$	−35.0789	−	20.2528i	−1.43090	−	0.826130i	−0.997189	+	0.0749222i	$0.976129\pi$
$602$	0.666884	−	16.4543i	0.0271802	−	0.670628i
$603$	13.1683			0.536254
$604$	−6.01859	+	1.10008i	−0.244893	+	0.0447616i
$605$	24.4830	−	14.1353i	0.995375	−	0.574680i
$606$	8.12608	+	5.14124i	0.330099	+	0.208849i
$607$	3.88198	−	2.24126i	0.157565	−	0.0909700i	−0.419144	−	0.907920i	$-0.637670\pi$
$607$	3.88198	−	2.24126i	0.157565	−	0.0909700i	0.576709	+	0.816950i	$0.304337\pi$
$608$	−35.3104	−	7.25107i	−1.43203	−	0.294070i
$609$	−12.0241	+	3.22185i	−0.487242	+	0.130556i
$610$	47.1885	−	10.6163i	1.91061	−	0.429842i
$611$	7.81389	−	6.61040i	0.316116	−	0.267428i
$612$	0.556121	+	1.17340i	0.0224799	+	0.0474318i
$613$	20.3210	+	11.7323i	0.820756	+	0.473864i	0.850677	−	0.525689i	$-0.176192\pi$
$613$	20.3210	+	11.7323i	0.820756	+	0.473864i	−0.0299212	+	0.999552i	$0.509526\pi$
$614$	−1.70165	+	0.892593i	−0.0686729	+	0.0360221i
$615$	−29.5370	+	17.0532i	−1.19105	+	0.687651i
$616$	6.18901	+	7.91095i	0.249362	+	0.318741i
$617$	−4.90337	+	18.2996i	−0.197402	+	0.736716i	0.794229	+	0.607618i	$0.207875\pi$
$617$	−4.90337	+	18.2996i	−0.197402	+	0.736716i	−0.991632	+	0.129098i	$0.958792\pi$
$618$	−4.72370	+	4.35572i	−0.190015	+	0.175213i
$619$		−	32.6575i		−	1.31262i	−0.754492	−	0.656309i	$-0.772117\pi$
$619$		−	32.6575i		−	1.31262i	0.754492	−	0.656309i	$-0.227883\pi$
$620$	−1.20749	−	6.60621i	−0.0484938	−	0.265312i
$621$	1.86056	+	6.94371i	0.0746617	+	0.278641i
$622$	−13.7217	−	26.1592i	−0.550191	−	1.04889i
$623$	26.8047			1.07391
$624$	−12.3691	+	7.41654i	−0.495161	+	0.296899i
$625$	27.5760			1.10304
$626$	−10.3633	−	19.7568i	−0.414202	−	0.789639i
$627$	−3.19021	−	11.9060i	−0.127405	−	0.475481i
$628$	−4.12371	+	0.753733i	−0.164554	+	0.0300772i
$629$		−	0.360596i		−	0.0143779i
$630$	7.43420	−	6.85507i	0.296186	−	0.273112i
$631$	3.96787	−	14.8083i	0.157958	−	0.589509i	−0.840875	−	0.541229i	$-0.817959\pi$
$631$	3.96787	−	14.8083i	0.157958	−	0.589509i	0.998834	−	0.0482802i	$-0.0153740\pi$
$632$	0.755320	+	0.0922425i	0.0300450	+	0.00366921i
$633$	17.2026	−	9.93192i	0.683742	−	0.394758i
$634$	15.4786	−	8.11925i	0.614734	−	0.322457i
$635$	0.489252	+	0.282470i	0.0194154	+	0.0112095i
$636$	9.17877	−	4.35020i	0.363962	−	0.172497i
$637$	10.7499	+	7.46285i	0.425925	+	0.295689i
$638$	−18.0960	+	4.07117i	−0.716427	+	0.161179i
$639$	−11.6842	+	3.13077i	−0.462220	+	0.123852i
$640$	−10.4764	−	42.8016i	−0.414118	−	1.69188i
$641$	−22.4789	+	12.9782i	−0.887863	+	0.512608i	−0.873243	−	0.487285i	$-0.837987\pi$
$641$	−22.4789	+	12.9782i	−0.887863	+	0.512608i	−0.0146201	+	0.999893i	$0.504654\pi$
$642$	−14.5788	−	9.22380i	−0.575381	−	0.364034i
$643$	10.3081	−	5.95139i	0.406512	−	0.234700i	−0.282778	−	0.959185i	$-0.591256\pi$
$643$	10.3081	−	5.95139i	0.406512	−	0.234700i	0.689290	+	0.724486i	$0.257923\pi$
$644$	4.74589	+	25.9650i	0.187014	+	1.02316i
$645$	−24.7039			−0.972713
$646$	0.236942	−	5.84617i	0.00932237	−	0.230015i
$647$	−12.4890	−	7.21051i	−0.490992	−	0.283474i	0.233994	−	0.972238i	$-0.424820\pi$
$647$	−12.4890	−	7.21051i	−0.490992	−	0.283474i	−0.724986	+	0.688764i	$0.758154\pi$
$648$	−2.25999	−	1.70072i	−0.0887808	−	0.0668105i
$649$	4.57977			0.179772
$650$	−47.7656	+	20.1865i	−1.87352	+	0.791779i
$651$	−1.11918	−	1.11918i	−0.0438641	−	0.0438641i
$652$	−33.9490	−	2.75640i	−1.32955	−	0.107949i
$653$	20.9843	−	5.62273i	0.821179	−	0.220034i	0.176317	−	0.984333i	$-0.443582\pi$
$653$	20.9843	−	5.62273i	0.821179	−	0.220034i	0.644862	+	0.764299i	$0.276915\pi$
$654$	9.17144	+	9.94627i	0.358632	+	0.388930i
$655$	−55.9526	−	55.9526i	−2.18625	−	2.18625i
$656$	20.4480	+	28.4392i	0.798359	+	1.11036i
$657$	0.257781	−	0.962053i	0.0100570	−	0.0375333i
$658$	6.22826	+	3.94052i	0.242803	+	0.153618i
$659$	24.2546	+	6.49899i	0.944823	+	0.253165i	0.698164	−	0.715938i	$-0.254001\pi$
$659$	24.2546	+	6.49899i	0.944823	+	0.253165i	0.246659	+	0.969102i	$0.420667\pi$
$660$	11.4817	−	9.75728i	0.446926	−	0.379802i
$661$	1.85165	−	3.20714i	0.0720206	−	0.124743i	−0.827766	−	0.561073i	$-0.810389\pi$
$661$	1.85165	−	3.20714i	0.0720206	−	0.124743i	0.899787	+	0.436330i	$0.143722\pi$
$662$	−24.1480	−	15.2781i	−0.938539	−	0.593799i
$663$	−1.51192	−	1.78718i	−0.0587182	−	0.0694084i
$664$	−30.9329	−	3.77764i	−1.20043	−	0.146601i
$665$	−44.0127	+	11.7932i	−1.70674	+	0.457319i
$666$	0.364858	+	0.695569i	0.0141380	+	0.0269527i
$667$	−47.0819	−	12.6156i	−1.82302	−	0.488476i
$668$	−2.74731	+	7.69758i	−0.106297	+	0.297828i
$669$	−10.1929	−	17.6545i	−0.394079	−	0.682564i
$670$	2.93730	−	72.4732i	0.113478	−	2.79989i
$671$	12.0106	−	12.0106i	0.463663	−	0.463663i
$672$	−7.76561	−	6.89572i	−0.299565	−	0.266008i
$673$	10.5912	+	6.11481i	0.408259	+	0.235709i	0.690042	−	0.723770i	$-0.257592\pi$
$673$	10.5912	+	6.11481i	0.408259	+	0.235709i	−0.281782	+	0.959478i	$0.590926\pi$
$674$	11.5273	+	21.9758i	0.444016	+	0.846475i
$675$	−7.19114	−	7.19114i	−0.276787	−	0.276787i
$676$	18.1200	−	18.6458i	0.696923	−	0.717146i
$677$	−10.0882	+	10.0882i	−0.387722	+	0.387722i	−0.873874	−	0.486152i	$-0.838400\pi$
$677$	−10.0882	+	10.0882i	−0.387722	+	0.387722i	0.486152	+	0.873874i	$0.338400\pi$
$678$	7.19153	−	23.0597i	0.276189	−	0.885604i
$679$	9.76979	−	16.9218i	0.374930	−	0.649398i
$680$	6.58198	−	2.79895i	0.252408	−	0.107335i
$681$	−15.9131	−	15.9131i	−0.609791	−	0.609791i
$682$	−1.59871	−	1.73377i	−0.0612177	−	0.0663896i
$683$	−5.91896	+	3.41731i	−0.226483	+	0.130760i	−0.608948	−	0.793210i	$-0.708408\pi$
$683$	−5.91896	+	3.41731i	−0.226483	+	0.130760i	0.382466	+	0.923970i	$0.375075\pi$
$684$	5.45822	+	11.5167i	0.208700	+	0.440350i
$685$	−22.3404	+	83.3755i	−0.853582	+	3.18561i
$686$	−8.21651	+	26.3463i	−0.313708	+	1.00591i
$687$	−0.153587	−	0.573195i	−0.00585971	−	0.0218688i
$688$	2.52705	+	25.2447i	0.0963431	+	0.962444i
$689$	−13.9800	+	11.8268i	−0.532597	+	0.450567i
$690$	38.6306	−	8.69097i	1.47064	−	0.330859i
$691$	4.82955	+	2.78834i	0.183725	+	0.106074i	0.589042	−	0.808103i	$-0.299505\pi$
$691$	4.82955	+	2.78834i	0.183725	+	0.106074i	−0.405317	+	0.914176i	$0.632839\pi$
$692$	−17.0503	+	14.4895i	−0.648153	+	0.550807i
$693$	0.919112	−	3.43017i	0.0349142	−	0.130302i
$694$	0.999776	+	4.44391i	0.0379510	+	0.168689i
$695$	−6.54490	−	1.75370i	−0.248262	−	0.0665216i
$696$	17.6487	−	7.50501i	0.668974	−	0.284477i
$697$	−4.02019	+	4.02019i	−0.152275	+	0.152275i
$698$	43.9837	+	1.78264i	1.66481	+	0.0674738i
$699$	−4.02123	−	15.0074i	−0.152097	−	0.567633i
$700$	−24.1809	−	28.4545i	−0.913951	−	1.07548i
$701$	−30.7211	+	30.7211i	−1.16032	+	1.16032i	−0.175913	+	0.984406i	$0.556288\pi$
$701$	−30.7211	+	30.7211i	−1.16032	+	1.16032i	−0.984406	+	0.175913i	$0.943712\pi$
$702$	4.72471	+	1.91758i	0.178323	+	0.0723743i
$703$		−	3.53918i		−	0.133483i
$704$	−11.1454	−	10.7350i	−0.420058	−	0.404589i
$705$	5.52808	−	9.57491i	0.208199	−	0.360612i
$706$	−6.90124	−	7.48428i	−0.259732	−	0.281675i
$707$		−	12.4831i		−	0.469474i
$708$	−4.65813	+	0.851414i	−0.175063	+	0.0319981i
$709$	−1.03390	−	1.79076i	−0.0388288	−	0.0672534i	0.845958	−	0.533250i	$-0.179029\pi$
$709$	−1.03390	−	1.79076i	−0.0388288	−	0.0672534i	−0.884787	+	0.465996i	$0.845696\pi$
$710$	14.6243	+	65.0038i	0.548842	+	2.43955i
$711$	−0.134515	−	0.232987i	−0.00504471	−	0.00873769i
$712$	−40.8905	+	5.77394i	−1.53244	+	0.216388i
$713$	−1.60403	−	5.98631i	−0.0600713	−	0.224189i
$714$	0.901271	−	1.42452i	0.0337292	−	0.0533113i
$715$	−15.4908	+	22.3137i	−0.579321	+	0.834483i
$716$	−0.255549	+	0.716011i	−0.00955031	+	0.0267586i
$717$	−7.77462	+	13.4660i	−0.290348	+	0.502898i
$718$	15.1147	+	4.71376i	0.564076	+	0.175916i
$719$	18.8419	+	32.6351i	0.702683	+	1.21708i	0.967521	+	0.252790i	$0.0813480\pi$
$719$	18.8419	+	32.6351i	0.702683	+	1.21708i	−0.264838	+	0.964293i	$0.585319\pi$
$720$	−9.86423	+	12.0588i	−0.367618	+	0.449404i
$721$	8.05702	+	2.15887i	0.300059	+	0.0804006i
$722$	1.23741	−	30.5310i	0.0460515	−	1.13625i
$723$	16.3371			0.607582
$724$	−25.3473	+	4.63298i	−0.942023	+	0.172183i
$725$	66.6069	−	17.8473i	2.47372	−	0.662831i
$726$	−3.05613	+	9.79950i	−0.113423	+	0.363694i
$727$			30.5222i			1.13201i	0.824403	+	0.566003i	$0.191511\pi$
$727$			30.5222i			1.13201i	−0.824403	+	0.566003i	$0.808489\pi$
$728$	16.7214	+	8.42174i	0.619736	+	0.312130i
$729$			1.00000i			0.0370370i
$730$	−5.23728	−	1.63333i	−0.193840	−	0.0604521i
$731$	−3.97772	+	1.06583i	−0.147121	+	0.0394210i
$732$	−9.98322	+	14.4489i	−0.368990	+	0.534048i
$733$	39.9129			1.47422			0.737108	−	0.675775i	$-0.236191\pi$
$733$	39.9129			1.47422			0.737108	+	0.675775i	$0.236191\pi$
$734$	23.7873	+	0.964087i	0.878006	+	0.0355851i
$735$	13.6547	+	3.65876i	0.503661	+	0.134956i
$736$	−12.8329	−	38.5872i	−0.473027	−	1.42234i
$737$	−12.7358	−	22.0590i	−0.469128	−	0.812553i
$738$	3.68700	−	11.8224i	0.135720	−	0.435189i
$739$	−18.6042	+	32.2234i	−0.684366	+	1.18536i	0.289270	+	0.957248i	$0.406587\pi$
$739$	−18.6042	+	32.2234i	−0.684366	+	1.18536i	−0.973636	+	0.228109i	$0.926746\pi$
$740$	3.90953	−	1.85289i	0.143717	−	0.0681136i
$741$	−14.8392	−	17.5408i	−0.545132	−	0.644379i
$742$	−11.1431	−	7.05009i	−0.409078	−	0.258817i
$743$	−9.92220	−	37.0301i	−0.364010	−	1.35850i	−0.868758	−	0.495237i	$-0.835081\pi$
$743$	−9.92220	−	37.0301i	−0.364010	−	1.35850i	0.504748	−	0.863267i	$-0.331586\pi$
$744$	1.94839	+	1.46623i	0.0714313	+	0.0537544i
$745$	34.4383	+	59.6488i	1.26172	+	2.18536i
$746$	−0.138807	+	0.0312283i	−0.00508208	+	0.00114335i
$747$	5.50884	+	9.54160i	0.201558	+	0.349109i
$748$	1.42777	−	2.06645i	0.0522046	−	0.0755569i
$749$			22.3956i			0.818318i
$750$	−20.9345	+	19.3037i	−0.764420	+	0.704870i
$751$	−26.9772	+	46.7258i	−0.984411	+	1.70505i	−0.339884	+	0.940467i	$0.610388\pi$
$751$	−26.9772	+	46.7258i	−0.984411	+	1.70505i	−0.644526	+	0.764582i	$0.722945\pi$
$752$	−10.3500	−	4.66964i	−0.377426	−	0.170284i
$753$			8.81830i			0.321357i
$754$	−27.2782	+	21.2429i	−0.993413	+	0.773620i
$755$	8.42512	−	8.42512i	0.306621	−	0.306621i
$756$	−0.297142	+	3.65973i	−0.0108070	+	0.133103i
$757$	4.05347	+	15.1277i	0.147326	+	0.549827i	0.999641	+	0.0267984i	$0.00853122\pi$
$757$	4.05347	+	15.1277i	0.147326	+	0.549827i	−0.852315	+	0.523029i	$0.824802\pi$
$758$	0.863535	−	21.3064i	0.0313650	−	0.773882i
$759$	9.83238	−	9.83238i	0.356893	−	0.356893i
$760$	64.6009	−	27.4711i	2.34332	−	0.996481i
$761$	45.1083	+	12.0867i	1.63517	+	0.438143i	0.955409	−	0.295287i	$-0.0954151\pi$
$761$	45.1083	+	12.0867i	1.63517	+	0.438143i	0.679765	+	0.733430i	$0.262082\pi$
$762$	−0.200127	+	0.0450238i	−0.00724982	+	0.00163104i
$763$	4.54574	−	16.9649i	0.164567	−	0.614172i
$764$	−1.53367	+	18.8893i	−0.0554861	+	0.683392i
$765$	−2.18996	−	1.26437i	−0.0791782	−	0.0457136i
$766$	0.726580	+	3.22958i	0.0262524	+	0.116689i
$767$	7.72228	−	3.63886i	0.278835	−	0.131392i
$768$	13.3318	+	8.84663i	0.481070	+	0.319225i
$769$	7.50985	+	28.0271i	0.270812	+	1.01068i	0.958596	+	0.284769i	$0.0919168\pi$
$769$	7.50985	+	28.0271i	0.270812	+	1.01068i	−0.687784	+	0.725915i	$0.741416\pi$
$770$	−18.6734	−	5.82358i	−0.672942	−	0.209867i
$771$	0.428498	−	1.59917i	0.0154320	−	0.0575929i
$772$	2.13202	−	5.97360i	0.0767329	−	0.214995i
$773$	−21.1367	+	12.2033i	−0.760234	+	0.438921i	−0.829380	−	0.558685i	$-0.811306\pi$
$773$	−21.1367	+	12.2033i	−0.760234	+	0.438921i	0.0691459	+	0.997607i	$0.477973\pi$
$774$	6.59436	−	6.08065i	0.237029	−	0.218564i
$775$	6.19963	+	6.19963i	0.222697	+	0.222697i
$776$	−11.2587	+	27.9186i	−0.404164	+	1.00222i
$777$	0.509826	−	0.883045i	0.0182899	−	0.0316790i
$778$	6.25163	+	1.94967i	0.224132	+	0.0698989i
$779$	−39.4573	+	39.4573i	−1.41371	+	1.41371i
$780$	11.6075	−	25.5753i	0.415616	−	0.915742i
$781$	16.5450	+	16.5450i	0.592026	+	0.592026i
$782$	5.84518	−	3.06607i	0.209023	−	0.109642i
$783$	−5.87210	−	3.39026i	−0.209852	−	0.121158i
$784$	2.34207	−	14.3279i	0.0836453	−	0.511710i
$785$	5.77257	−	5.77257i	0.206032	−	0.206032i
$786$	28.7081	+	1.16352i	1.02398	+	0.0415015i
$787$	26.8284	+	46.4682i	0.956331	+	1.65641i	0.731293	+	0.682063i	$0.238917\pi$
$787$	26.8284	+	46.4682i	0.956331	+	1.65641i	0.225037	+	0.974350i	$0.427750\pi$
$788$	−36.7122	+	17.3994i	−1.30782	+	0.619828i
$789$	15.5320	+	4.16178i	0.552953	+	0.148163i
$790$	−1.31228	+	0.688350i	−0.0466887	+	0.0244904i
$791$	−30.2889	+	8.11590i	−1.07695	+	0.288568i
$792$	−0.663218	+	5.43071i	−0.0235664	+	0.192972i
$793$	10.7089	−	29.7949i	0.380284	−	1.05805i
$794$	−0.839458	+	1.32682i	−0.0297912	+	0.0470871i
$795$	−9.89043	+	17.1307i	−0.350777	+	0.607564i
$796$	2.80486	−	34.5458i	0.0994155	−	1.22444i
$797$	−16.8632	−	4.51847i	−0.597324	−	0.160052i	−0.0525254	−	0.998620i	$-0.516727\pi$
$797$	−16.8632	−	4.51847i	−0.597324	−	0.160052i	−0.544798	+	0.838567i	$0.683394\pi$
$798$	8.84579	−	13.9814i	0.313138	−	0.494935i
$799$	0.477008	−	1.78022i	0.0168753	−	0.0629796i
$800$	43.0172	+	38.1985i	1.52089	+	1.35052i
$801$	10.3240	+	10.3240i	0.364782	+	0.364782i
$802$	10.8666	−	10.0201i	0.383715	−	0.353823i
$803$	−1.86091	+	0.498629i	−0.0656700	+	0.0175962i
$804$	17.0546	+	20.0687i	0.601470	+	0.707770i
$805$	−36.3470	−	36.3470i	−1.28106	−	1.28106i
$806$	−4.07327	−	1.65318i	−0.143475	−	0.0582309i
$807$	20.4540			0.720013
$808$	2.68895	+	19.0429i	0.0945969	+	0.669926i
$809$	38.1519	+	22.0270i	1.34135	+	0.774428i	0.987005	−	0.160688i	$-0.0513713\pi$
$809$	38.1519	+	22.0270i	1.34135	+	0.774428i	0.354343	+	0.935116i	$0.384705\pi$
$810$	5.50362	+	0.223059i	0.193378	+	0.00783749i
$811$	−23.8046			−0.835894			−0.417947	−	0.908471i	$-0.637250\pi$
$811$	−23.8046			−0.835894			−0.417947	+	0.908471i	$0.637250\pi$
$812$	−20.4829	−	14.1523i	−0.718810	−	0.496648i
$813$	−0.0272728	+	0.0157460i	−0.000956499	+	0.000552235i
$814$	0.812316	−	1.28392i	0.0284716	−	0.0450013i
$815$	57.4440	−	33.1653i	2.01218	−	1.16173i
$816$	−1.06803	+	2.36724i	−0.0373887	+	0.0828700i
$817$	−39.0405	+	10.4609i	−1.36586	+	0.365980i
$818$	9.30370	+	41.3541i	0.325296	+	1.44591i
$819$	−1.17567	−	6.51415i	−0.0410811	−	0.227623i
$820$	−64.2436	−	22.9289i	−2.24348	−	0.800713i
$821$	31.3260	+	18.0861i	1.09329	+	0.631209i	0.934449	−	0.356096i	$-0.115892\pi$
$821$	31.3260	+	18.0861i	1.09329	+	0.631209i	0.158837	+	0.987305i	$0.449226\pi$
$822$	−14.5587	−	27.7549i	−0.507793	−	0.968062i
$823$	43.2718	−	24.9830i	1.50836	−	0.870851i	0.508406	−	0.861117i	$-0.330235\pi$
$823$	43.2718	−	24.9830i	1.50836	−	0.870851i	0.999953	−	0.00973390i	$-0.00309845\pi$
$824$	−12.7560	−	1.55781i	−0.444376	−	0.0542689i
$825$	−5.09137	+	19.0013i	−0.177259	+	0.661539i
$826$	4.16715	+	4.51920i	0.144994	+	0.157243i
$827$		−	0.994536i		−	0.0345834i	−0.999850	−	0.0172917i	$-0.994496\pi$
$827$		−	0.994536i		−	0.0345834i	0.999850	−	0.0172917i	$-0.00550439\pi$
$828$	−8.17269	+	11.8285i	−0.284021	+	0.411070i
$829$	−8.42866	−	31.4562i	−0.292740	−	1.09252i	−0.942996	−	0.332804i	$-0.892005\pi$
$829$	−8.42866	−	31.4562i	−0.292740	−	1.09252i	0.650256	−	0.759715i	$-0.274661\pi$
$830$	53.7422	−	28.1903i	1.86542	−	0.978498i
$831$	−11.0735			−0.384134
$832$	−27.3226	−	9.24543i	−0.947239	−	0.320527i
$833$	2.35648			0.0816472
$834$	2.17873	−	1.14285i	0.0754433	−	0.0395735i
$835$	−4.11952	−	15.3742i	−0.142562	−	0.532048i
$836$	14.0133	−	20.2818i	0.484661	−	0.701460i
$837$		−	0.862121i		−	0.0297993i
$838$	−12.3473	−	13.3904i	−0.426529	−	0.462563i
$839$	14.7634	−	55.0979i	0.509691	−	1.90219i	0.0862354	−	0.996275i	$-0.472516\pi$
$839$	14.7634	−	55.0979i	0.509691	−	1.90219i	0.423455	−	0.905917i	$-0.360817\pi$
$840$	20.0755	+	2.45170i	0.692671	+	0.0845915i
$841$	14.7011	−	8.48770i	0.506935	−	0.292679i
$842$	19.4570	+	37.0929i	0.670532	+	1.27831i
$843$	21.2639	+	12.2767i	0.732367	+	0.422833i
$844$	37.4160	+	13.3540i	1.28791	+	0.459664i
$845$	−8.39074	+	49.9329i	−0.288650	+	1.71774i
$846$	0.881139	+	3.91658i	0.0302942	+	0.134655i
$847$	12.8716	−	3.44895i	0.442275	−	0.118507i
$848$	18.5175	+	8.35458i	0.635893	+	0.286897i
$849$	−17.6991	+	10.2186i	−0.607432	+	0.350701i
$850$	−4.99254	+	7.89105i	−0.171243	+	0.270661i
$851$	3.45767	−	1.99629i	0.118527	−	0.0684319i
$852$	−19.9039	−	13.7522i	−0.681897	−	0.471144i
$853$	19.9323			0.682470			0.341235	−	0.939978i	$-0.389155\pi$
$853$	19.9323			0.682470			0.341235	+	0.939978i	$0.389155\pi$
$854$	22.7802	+	0.923270i	0.779523	+	0.0315936i
$855$	−21.4940	−	12.4096i	−0.735081	−	0.424399i
$856$	−4.82419	−	34.1645i	−0.164887	−	1.16772i
$857$	−23.8425			−0.814443			−0.407222	−	0.913329i	$-0.633502\pi$
$857$	−23.8425			−0.814443			−0.407222	+	0.913329i	$0.633502\pi$
$858$	−1.35727	−	9.76925i	−0.0463366	−	0.333517i
$859$	20.2501	+	20.2501i	0.690926	+	0.690926i	0.962436	−	0.271510i	$-0.0875229\pi$
$859$	20.2501	+	20.2501i	0.690926	+	0.690926i	−0.271510	+	0.962436i	$0.587523\pi$
$860$	−31.9947	−	37.6492i	−1.09101	−	1.28383i
$861$	−15.5287	+	4.16091i	−0.529217	+	0.141803i
$862$	−29.9749	+	27.6398i	−1.02095	+	0.941416i
$863$	12.7647	+	12.7647i	0.434515	+	0.434515i	0.890161	−	0.455646i	$-0.150592\pi$
$863$	12.7647	+	12.7647i	0.434515	+	0.434515i	−0.455646	+	0.890161i	$0.650592\pi$
$864$	−0.335045	−	5.64692i	−0.0113985	−	0.192112i
$865$	11.2778	−	42.0895i	0.383458	−	1.43109i
$866$	5.40664	−	8.54556i	0.183725	−	0.290390i
$867$	16.0136	+	4.29082i	0.543849	+	0.145724i
$868$	0.256173	−	3.15513i	0.00869507	−	0.107092i
$869$	−0.260194	+	0.450669i	−0.00882647	+	0.0152879i
$870$	−19.9685	+	31.5616i	−0.676996	+	1.07004i
$871$	−39.0017	−	27.0761i	−1.32152	−	0.917437i
$872$	−3.28014	+	26.8592i	−0.111080	+	0.909566i
$873$	10.2805	−	2.75464i	0.347941	−	0.0932305i
$874$	57.3693	−	30.0929i	1.94054	−	1.01791i
$875$	35.7071	+	9.56770i	1.20712	+	0.323447i
$876$	1.80005	−	0.853118i	0.0608180	−	0.0288242i
$877$	18.9134	+	32.7589i	0.638659	+	1.10619i	0.985727	+	0.168351i	$0.0538441\pi$
$877$	18.9134	+	32.7589i	0.638659	+	1.10619i	−0.347068	+	0.937840i	$0.612823\pi$
$878$	32.0269	+	1.29804i	1.08086	+	0.0438066i
$879$	12.0828	−	12.0828i	0.407542	−	0.407542i
$880$	29.7406	+	4.86147i	1.00256	+	0.163880i
$881$	−16.8302	−	9.71694i	−0.567025	−	0.327372i	0.188935	−	0.981990i	$-0.439496\pi$
$881$	−16.8302	−	9.71694i	−0.567025	−	0.327372i	−0.755960	+	0.654618i	$0.772830\pi$
$882$	−4.54551	+	2.38433i	−0.153055	+	0.0802846i
$883$	7.85171	+	7.85171i	0.264231	+	0.264231i	0.826770	−	0.562539i	$-0.190176\pi$
$883$	7.85171	+	7.85171i	0.264231	+	0.264231i	−0.562539	+	0.826770i	$0.690176\pi$
$884$	0.765574	−	4.61883i	0.0257490	−	0.155348i
$885$	6.52067	−	6.52067i	0.219190	−	0.219190i
$886$	−3.40443	−	1.06172i	−0.114374	−	0.0356693i
$887$	−2.36305	+	4.09293i	−0.0793436	+	0.137427i	−0.902967	−	0.429710i	$-0.858616\pi$
$887$	−2.36305	+	4.09293i	−0.0793436	+	0.137427i	0.823623	+	0.567137i	$0.191949\pi$
$888$	−0.587524	+	1.45690i	−0.0197160	+	0.0488905i
$889$	0.188297	+	0.188297i	0.00631527	+	0.00631527i
$890$	59.1225	−	54.5168i	1.98179	−	1.82741i
$891$	1.67516	−	0.967155i	0.0561200	−	0.0324009i
$892$	13.7049	−	38.3990i	0.458872	−	1.28569i
$893$	4.68174	−	17.4725i	0.156669	−	0.584695i
$894$	−23.8749	−	7.44575i	−0.798496	−	0.249023i
$895$	−0.383188	−	1.43008i	−0.0128086	−	0.0478022i
$896$	0.451763	−	20.7658i	0.0150923	−	0.693737i
$897$	8.76676	−	24.3914i	0.292714	−	0.814406i
$898$	10.6018	+	47.1243i	0.353788	+	1.57256i
$899$	5.06246	+	2.92281i	0.168843	+	0.0974813i
$900$	1.64600	−	20.2729i	0.0548668	−	0.675764i
$901$	−0.853428	+	3.18504i	−0.0284318	+	0.106109i
$902$	−23.3703	+	5.25777i	−0.778147	+	0.175065i
$903$	−11.2477	−	3.01382i	−0.374301	−	0.100294i
$904$	44.4575	−	18.9053i	1.47863	−	0.628779i
$905$	35.4823	−	35.4823i	1.17947	−	1.17947i
$906$	−0.175199	+	4.32274i	−0.00582058	+	0.143614i
$907$	−1.14380	−	4.26871i	−0.0379792	−	0.141740i	0.944333	−	0.328992i	$-0.106709\pi$
$907$	−1.14380	−	4.26871i	−0.0379792	−	0.141740i	−0.982312	+	0.187251i	$0.940042\pi$
$908$	3.64240	−	44.8614i	0.120877	−	1.48878i
$909$	4.80795	−	4.80795i	0.159470	−	0.159470i
$910$	−36.1137	+	5.01739i	−1.19716	+	0.166325i
$911$			9.41465i			0.311921i	0.987763	+	0.155961i	$0.0498473\pi$
$911$			9.41465i			0.311921i	−0.987763	+	0.155961i	$0.950153\pi$
$912$	−10.4825	+	23.2340i	−0.347112	+	0.769355i
$913$	10.6558	−	18.4564i	0.352656	−	0.610818i
$914$	5.80474	−	5.35254i	0.192004	−	0.177046i
$915$		−	34.2013i		−	1.13066i
$916$	0.674646	−	0.976431i	0.0222909	−	0.0322622i
$917$	−18.6493	−	32.3015i	−0.615853	−	1.06669i
$918$	0.895796	−	0.201533i	0.0295657	−	0.00665158i
$919$	5.62333	+	9.73989i	0.185496	+	0.321289i	0.943744	−	0.330678i	$-0.107277\pi$
$919$	5.62333	+	9.73989i	0.185496	+	0.321289i	−0.758247	+	0.651967i	$0.773944\pi$
$920$	63.2768	+	47.6179i	2.08617	+	1.56992i
$921$	0.351667	+	1.31244i	0.0115878	+	0.0432463i
$922$	−26.2131	−	16.5846i	−0.863282	−	0.546185i
$923$	41.0436	+	14.7519i	1.35097	+	0.485564i
$924$	6.41803	−	3.04177i	0.211138	−	0.100067i
$925$	−2.82415	+	4.89158i	−0.0928576	+	0.160834i
$926$	−12.2211	+	39.1871i	−0.401610	+	1.28777i
$927$	2.27172	+	3.93473i	0.0746130	+	0.129233i
$928$	34.2952	+	17.1771i	1.12579	+	0.563866i
$929$	−8.47417	−	2.27065i	−0.278029	−	0.0744975i	0.117110	−	0.993119i	$-0.462637\pi$
$929$	−8.47417	−	2.27065i	−0.278029	−	0.0744975i	−0.395139	+	0.918621i	$0.629304\pi$
$930$	−4.74479	−	0.192304i	−0.155588	−	0.00630589i
$931$	23.1284			0.758002
$932$	17.6636	−	25.5650i	0.578592	−	0.837409i
$933$	−20.1760	+	5.40613i	−0.660531	+	0.176989i
$934$	−46.6995	−	14.5640i	−1.52805	−	0.476547i
$935$			4.89138i			0.159965i
$936$	3.19668	+	9.68407i	0.104487	+	0.316534i
$937$		−	16.7456i		−	0.547054i	−0.961864	−	0.273527i	$-0.911810\pi$
$937$		−	16.7456i		−	0.547054i	0.961864	−	0.273527i	$-0.0881902\pi$
$938$	10.1789	−	32.6389i	0.332354	−	1.06570i
$939$	−15.2379	+	4.08298i	−0.497270	+	0.133243i
$940$	21.7519	−	3.97583i	0.709470	−	0.129677i
$941$	−24.4051			−0.795584			−0.397792	−	0.917476i	$-0.630223\pi$
$941$	−24.4051			−0.795584			−0.397792	+	0.917476i	$0.630223\pi$
$942$	−0.120039	+	2.96178i	−0.00391109	+	0.0965000i
$943$	−60.8047	−	16.2926i	−1.98007	−	0.530559i
$944$	−7.33045	−	5.99640i	−0.238586	−	0.195166i
$945$	−3.57525	−	6.19252i	−0.116303	−	0.201443i
$946$	−16.5638	−	5.16569i	−0.538537	−	0.167951i
$947$	15.0297	−	26.0322i	0.488400	−	0.845934i	−0.511511	−	0.859277i	$-0.670914\pi$
$947$	15.0297	−	26.0322i	0.488400	−	0.845934i	0.999911	+	0.0133428i	$0.00424727\pi$
$948$	0.180863	−	0.506752i	0.00587415	−	0.0164585i
$949$	−2.74163	+	2.31936i	−0.0889970	+	0.0752897i
$950$	−49.0008	+	77.4491i	−1.58980	+	2.51278i
$951$	−3.19885	−	11.9383i	−0.103730	−	0.387125i
$952$	3.33826	−	0.471379i	0.108194	−	0.0152775i
$953$	6.49208	+	11.2446i	0.210299	+	0.364249i	0.951808	−	0.306694i	$-0.0992228\pi$
$953$	6.49208	+	11.2446i	0.210299	+	0.364249i	−0.741509	+	0.670943i	$0.765890\pi$
$954$	−1.57647	−	7.00726i	−0.0510401	−	0.226869i
$955$	−18.4533	−	31.9620i	−0.597134	−	1.03427i
$956$	−30.5917	+	5.59156i	−0.989405	+	0.180844i
$957$			13.1156i			0.423968i
$958$	33.8956	+	36.7592i	1.09512	+	1.18764i
$959$	−20.3433	+	35.2356i	−0.656919	+	1.13782i
$960$	−31.1533	+	0.584367i	−1.00547	+	0.0188604i
$961$		−	30.2567i		−	0.976024i
$962$	0.349565	−	2.81034i	0.0112704	−	0.0906089i
$963$	−8.62585	+	8.62585i	−0.277964	+	0.277964i
$964$	21.1586	+	24.8981i	0.681473	+	0.801912i
$965$	3.19689	+	11.9310i	0.102912	+	0.384072i
$966$	18.6489	+	0.755829i	0.600018	+	0.0243184i
$967$	29.0068	−	29.0068i	0.932797	−	0.932797i	−0.0650829	−	0.997880i	$-0.520731\pi$
$967$	29.0068	−	29.0068i	0.932797	−	0.932797i	0.997880	+	0.0650829i	$0.0207312\pi$
$968$	−18.8927	+	8.03401i	−0.607235	+	0.258223i
$969$	−3.99629	−	1.07080i	−0.128379	−	0.0343991i
$970$	−12.8674	−	57.1942i	−0.413146	−	1.83640i
$971$	0.565773	−	2.11149i	0.0181565	−	0.0677611i	−0.956253	−	0.292540i	$-0.905499\pi$
$971$	0.565773	−	2.11149i	0.0181565	−	0.0677611i	0.974410	+	0.224779i	$0.0721661\pi$
$972$	−1.52402	+	1.29513i	−0.0488830	+	0.0415413i
$973$	−2.76596	−	1.59693i	−0.0886726	−	0.0511952i
$974$	9.62444	−	2.16527i	0.308387	−	0.0693799i
$975$	6.51255	+	36.0848i	0.208568	+	1.15564i
$976$	−34.9500	+	3.49859i	−1.11872	+	0.111987i
$977$	−3.46230	−	12.9215i	−0.110769	−	0.413395i	0.888167	−	0.459521i	$-0.151979\pi$
$977$	−3.46230	−	12.9215i	−0.110769	−	0.413395i	−0.998936	+	0.0461261i	$0.985312\pi$
$978$	−7.17054	+	22.9924i	−0.229288	+	0.735216i
$979$	7.30949	−	27.2794i	0.233612	−	0.871853i
$980$	12.1085	+	25.5486i	0.386793	+	0.816121i
$981$	8.28501	−	4.78335i	0.264520	−	0.152721i
$982$	−0.498549	−	0.540668i	−0.0159093	−	0.0172534i
$983$	12.8098	+	12.8098i	0.408569	+	0.408569i	0.881239	−	0.472670i	$-0.156710\pi$
$983$	12.8098	+	12.8098i	0.408569	+	0.408569i	−0.472670	+	0.881239i	$0.656710\pi$
$984$	22.7927	−	9.69246i	0.726606	−	0.308984i
$985$	39.5586	−	68.5175i	1.26044	−	2.18315i
$986$	−1.85356	+	5.94345i	−0.0590293	+	0.189278i
$987$	3.68507	−	3.68507i	0.117297	−	0.117297i
$988$	7.51395	−	45.3329i	0.239051	−	1.44223i
$989$	−32.2409	−	32.2409i	−1.02520	−	1.02520i
$990$	−4.94920	−	9.43519i	−0.157296	−	0.299870i
$991$	53.8893	+	31.1130i	1.71185	+	0.988338i	0.932064	+	0.362293i	$0.118006\pi$
$991$	53.8893	+	31.1130i	1.71185	+	0.988338i	0.779787	+	0.626045i	$0.215327\pi$
$992$	0.288850	+	4.86833i	0.00917099	+	0.154570i
$993$	−14.2876	+	14.2876i	−0.453404	+	0.453404i
$994$	−1.27184	+	31.3806i	−0.0403402	+	0.995331i
$995$	33.7483	+	58.4539i	1.06989	+	1.85311i
$996$	−7.40694	+	20.7532i	−0.234698	+	0.657590i
$997$	−24.3535	−	6.52551i	−0.771284	−	0.206665i	−0.148345	−	0.988936i	$-0.547395\pi$
$997$	−24.3535	−	6.52551i	−0.771284	−	0.206665i	−0.622938	+	0.782271i	$0.714061\pi$
$998$	−24.4429	−	46.5981i	−0.773726	−	1.47504i
$999$	0.536475	−	0.143748i	0.0169733	−	0.00454799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.ch.a.19.47	✓	224
13.11	odd	12		624.2.cz.a.115.2	yes	224
16.11	odd	4		624.2.cz.a.331.2	yes	224
208.11	even	12	inner	624.2.ch.a.427.47	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.ch.a.19.47	✓	224	1.1	even	1	trivial
624.2.ch.a.427.47	yes	224	208.11	even	12	inner
624.2.cz.a.115.2	yes	224	13.11	odd	12
624.2.cz.a.331.2	yes	224	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25238 - 0.656929i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.13689 - 1.64544i) q^{4} +3.89484i q^{5} +(-0.958683 - 1.03968i) q^{6} +(-0.475163 + 1.77333i) q^{7} +(0.342870 - 2.80757i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.25238 - 0.656929i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.13689 - 1.64544i) q^{4} +3.89484i q^{5} +(-0.958683 - 1.03968i) q^{6} +(-0.475163 + 1.77333i) q^{7} +(0.342870 - 2.80757i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.55864 + 4.87781i) q^{10} +(1.67516 + 0.967155i) q^{11} +(-1.88363 - 0.672277i) q^{12} +(3.59307 + 0.299789i) q^{13} +(0.569871 + 2.53303i) q^{14} +(3.76213 - 1.00806i) q^{15} +(-1.41497 - 3.74137i) q^{16} +(0.562272 - 0.324628i) q^{17} +(-0.756124 + 1.19511i) q^{18} +(5.51859 - 3.18616i) q^{19} +(6.40875 + 4.42800i) q^{20} +1.83589 q^{21} +(2.73328 + 0.110779i) q^{22} +(6.22556 + 3.59433i) q^{23} +(-2.80064 + 0.395465i) q^{24} -10.1698 q^{25} +(4.69681 - 1.98494i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.37771 + 2.79793i) q^{28} +(-6.54948 + 1.75493i) q^{29} +(4.04938 - 3.73392i) q^{30} +(-0.609612 - 0.609612i) q^{31} +(-4.22989 - 3.75607i) q^{32} +(0.500636 - 1.86840i) q^{33} +(0.490918 - 0.775929i) q^{34} +(-6.90685 - 1.85069i) q^{35} +(-0.161852 + 1.99344i) q^{36} +(0.277700 - 0.480990i) q^{37} +(4.81826 - 7.61559i) q^{38} +(-0.640380 - 3.54823i) q^{39} +(10.9350 + 1.33543i) q^{40} +(-8.45842 + 2.26643i) q^{41} +(2.29922 - 1.20605i) q^{42} +(-6.12658 - 1.64161i) q^{43} +(3.49587 - 1.65684i) q^{44} +(-1.94742 - 3.37303i) q^{45} +(10.1580 + 0.411696i) q^{46} +(2.00724 - 2.00724i) q^{47} +(-3.24767 + 2.33510i) q^{48} +(3.14325 + 1.81476i) q^{49} +(-12.7364 + 6.68085i) q^{50} +(-0.459093 - 0.459093i) q^{51} +(4.57820 - 5.57136i) q^{52} +(-3.59120 + 3.59120i) q^{53} +(1.35008 + 0.421044i) q^{54} +(-3.76692 + 6.52449i) q^{55} +(4.81583 + 1.94208i) q^{56} +(-4.50591 - 4.50591i) q^{57} +(-7.04954 + 6.50037i) q^{58} +(2.05044 - 1.18382i) q^{59} +(2.61842 - 7.33643i) q^{60} +(2.27274 - 8.48197i) q^{61} +(-1.16393 - 0.362991i) q^{62} +(-0.475163 - 1.77333i) q^{63} +(-7.76488 - 1.92526i) q^{64} +(-1.16763 + 13.9944i) q^{65} +(-0.600422 - 2.66882i) q^{66} +(-11.4041 - 6.58414i) q^{67} +(0.105083 - 1.29425i) q^{68} +(1.86056 - 6.94371i) q^{69} +(-9.86574 + 2.21956i) q^{70} +(11.6842 + 3.13077i) q^{71} +(1.10685 + 2.60286i) q^{72} +(-0.704272 + 0.704272i) q^{73} +(0.0318079 - 0.784809i) q^{74} +(2.63214 + 9.82328i) q^{75} +(1.03137 - 12.7028i) q^{76} +(-2.51106 + 2.51106i) q^{77} +(-3.13293 - 4.02303i) q^{78} +0.269030i q^{79} +(14.5721 - 5.51109i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-9.10424 + 8.39500i) q^{82} -11.0177i q^{83} +(2.08720 - 3.02085i) q^{84} +(1.26437 + 2.18996i) q^{85} +(-8.75121 + 1.96882i) q^{86} +(3.39026 + 5.87210i) q^{87} +(3.28972 - 4.37152i) q^{88} +(-3.77886 - 14.1029i) q^{89} +(-4.65475 - 2.94499i) q^{90} +(-2.23892 + 6.22925i) q^{91} +(12.9920 - 6.15746i) q^{92} +(-0.431061 + 0.746619i) q^{93} +(1.19520 - 3.83243i) q^{94} +(12.4096 + 21.4940i) q^{95} +(-2.53330 + 5.05790i) q^{96} +(-10.2805 - 2.75464i) q^{97} +(5.12869 + 0.207863i) q^{98} -1.93431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q+O(q^{10}) \) 224 * q	\( 224 q - 8 q^{10} - 32 q^{14} - 48 q^{16} - 12 q^{20} + 8 q^{22} + 12 q^{24} - 224 q^{25} - 16 q^{26} - 52 q^{28} + 40 q^{32} + 64 q^{34} - 40 q^{38} - 40 q^{40} - 16 q^{43} + 24 q^{44} + 16 q^{46} - 16 q^{50} - 16 q^{52} - 32 q^{55} - 20 q^{56} - 32 q^{58} + 96 q^{59} - 64 q^{60} - 24 q^{68} - 48 q^{70} + 64 q^{71} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 76 q^{76} - 24 q^{78} + 100 q^{80} + 112 q^{81} + 48 q^{82} - 64 q^{86} - 60 q^{88} - 16 q^{89} + 40 q^{91} - 48 q^{92} + 64 q^{94} - 56 q^{98}+O(q^{100}) \) 224 * q - 8 * q^10 - 32 * q^14 - 48 * q^16 - 12 * q^20 + 8 * q^22 + 12 * q^24 - 224 * q^25 - 16 * q^26 - 52 * q^28 + 40 * q^32 + 64 * q^34 - 40 * q^38 - 40 * q^40 - 16 * q^43 + 24 * q^44 + 16 * q^46 - 16 * q^50 - 16 * q^52 - 32 * q^55 - 20 * q^56 - 32 * q^58 + 96 * q^59 - 64 * q^60 - 24 * q^68 - 48 * q^70 + 64 * q^71 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 76 * q^76 - 24 * q^78 + 100 * q^80 + 112 * q^81 + 48 * q^82 - 64 * q^86 - 60 * q^88 - 16 * q^89 + 40 * q^91 - 48 * q^92 + 64 * q^94 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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